Miscellaneous Application of Differential Equation
Differential Equation

87634 \(u \equiv u(x, y)=\sin (y+a x)-(y+a x)^{2}\), then it implies

1 \(u_{x x}=a^{2} \cdot u_{y y}\)
2 \(u_{y y}=a^{2} u_{z x}\)
3 \(u_{x x}=-a^{2} u_{y y}\)
4 \(u_{y y}=-a^{2} u_{x x}\)
Differential Equation

87635 The approximate value of \(\int_{1}^{3} \frac{d x}{2+3 x}\) using
Simpson's rule and dividing the interval \([1,3]\) into two equal parts is

1 \(\frac{1}{3} \log \left(\frac{11}{5}\right)\)
2 \(\frac{107}{110}\)
3 \(\frac{29}{110}\)
4 \(\frac{119}{440}\)
Differential Equation

87645 If \(x^{2}+y^{2}=1\), then

1 \(y\left(y^{\prime \prime}\right)-4\left(y^{\prime}\right)^2+1=0\)
2 \(y\left(y^{\prime \prime}\right)+\left(y^{\prime}\right)^2+1=0\)
3 \(y\left(y^{\prime \prime}\right)-\left(y^{\prime}\right)^2-1=0\)
4 \(y\left(y^{\prime \prime}\right)+2\left(y^{\prime}\right)^2+1=0\)
Differential Equation

87574 The solution of the differential equation \(2 x\left(\frac{d y}{d x}\right)-y=4\) represents a family of

1 Ellipses
2 Parabolas
3 Snaight lines
4 Circles
Differential Equation

87601 The value of \(\int_{0}^{1} x d x\) by Trapezoidal rule taking \(x=4\) is

1 0.34375
2 0.5
3 0.38387
4 0.35367
Differential Equation

87634 \(u \equiv u(x, y)=\sin (y+a x)-(y+a x)^{2}\), then it implies

1 \(u_{x x}=a^{2} \cdot u_{y y}\)
2 \(u_{y y}=a^{2} u_{z x}\)
3 \(u_{x x}=-a^{2} u_{y y}\)
4 \(u_{y y}=-a^{2} u_{x x}\)
Differential Equation

87635 The approximate value of \(\int_{1}^{3} \frac{d x}{2+3 x}\) using
Simpson's rule and dividing the interval \([1,3]\) into two equal parts is

1 \(\frac{1}{3} \log \left(\frac{11}{5}\right)\)
2 \(\frac{107}{110}\)
3 \(\frac{29}{110}\)
4 \(\frac{119}{440}\)
Differential Equation

87645 If \(x^{2}+y^{2}=1\), then

1 \(y\left(y^{\prime \prime}\right)-4\left(y^{\prime}\right)^2+1=0\)
2 \(y\left(y^{\prime \prime}\right)+\left(y^{\prime}\right)^2+1=0\)
3 \(y\left(y^{\prime \prime}\right)-\left(y^{\prime}\right)^2-1=0\)
4 \(y\left(y^{\prime \prime}\right)+2\left(y^{\prime}\right)^2+1=0\)
Differential Equation

87574 The solution of the differential equation \(2 x\left(\frac{d y}{d x}\right)-y=4\) represents a family of

1 Ellipses
2 Parabolas
3 Snaight lines
4 Circles
Differential Equation

87601 The value of \(\int_{0}^{1} x d x\) by Trapezoidal rule taking \(x=4\) is

1 0.34375
2 0.5
3 0.38387
4 0.35367
Differential Equation

87634 \(u \equiv u(x, y)=\sin (y+a x)-(y+a x)^{2}\), then it implies

1 \(u_{x x}=a^{2} \cdot u_{y y}\)
2 \(u_{y y}=a^{2} u_{z x}\)
3 \(u_{x x}=-a^{2} u_{y y}\)
4 \(u_{y y}=-a^{2} u_{x x}\)
Differential Equation

87635 The approximate value of \(\int_{1}^{3} \frac{d x}{2+3 x}\) using
Simpson's rule and dividing the interval \([1,3]\) into two equal parts is

1 \(\frac{1}{3} \log \left(\frac{11}{5}\right)\)
2 \(\frac{107}{110}\)
3 \(\frac{29}{110}\)
4 \(\frac{119}{440}\)
Differential Equation

87645 If \(x^{2}+y^{2}=1\), then

1 \(y\left(y^{\prime \prime}\right)-4\left(y^{\prime}\right)^2+1=0\)
2 \(y\left(y^{\prime \prime}\right)+\left(y^{\prime}\right)^2+1=0\)
3 \(y\left(y^{\prime \prime}\right)-\left(y^{\prime}\right)^2-1=0\)
4 \(y\left(y^{\prime \prime}\right)+2\left(y^{\prime}\right)^2+1=0\)
Differential Equation

87574 The solution of the differential equation \(2 x\left(\frac{d y}{d x}\right)-y=4\) represents a family of

1 Ellipses
2 Parabolas
3 Snaight lines
4 Circles
Differential Equation

87601 The value of \(\int_{0}^{1} x d x\) by Trapezoidal rule taking \(x=4\) is

1 0.34375
2 0.5
3 0.38387
4 0.35367
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Differential Equation

87634 \(u \equiv u(x, y)=\sin (y+a x)-(y+a x)^{2}\), then it implies

1 \(u_{x x}=a^{2} \cdot u_{y y}\)
2 \(u_{y y}=a^{2} u_{z x}\)
3 \(u_{x x}=-a^{2} u_{y y}\)
4 \(u_{y y}=-a^{2} u_{x x}\)
Differential Equation

87635 The approximate value of \(\int_{1}^{3} \frac{d x}{2+3 x}\) using
Simpson's rule and dividing the interval \([1,3]\) into two equal parts is

1 \(\frac{1}{3} \log \left(\frac{11}{5}\right)\)
2 \(\frac{107}{110}\)
3 \(\frac{29}{110}\)
4 \(\frac{119}{440}\)
Differential Equation

87645 If \(x^{2}+y^{2}=1\), then

1 \(y\left(y^{\prime \prime}\right)-4\left(y^{\prime}\right)^2+1=0\)
2 \(y\left(y^{\prime \prime}\right)+\left(y^{\prime}\right)^2+1=0\)
3 \(y\left(y^{\prime \prime}\right)-\left(y^{\prime}\right)^2-1=0\)
4 \(y\left(y^{\prime \prime}\right)+2\left(y^{\prime}\right)^2+1=0\)
Differential Equation

87574 The solution of the differential equation \(2 x\left(\frac{d y}{d x}\right)-y=4\) represents a family of

1 Ellipses
2 Parabolas
3 Snaight lines
4 Circles
Differential Equation

87601 The value of \(\int_{0}^{1} x d x\) by Trapezoidal rule taking \(x=4\) is

1 0.34375
2 0.5
3 0.38387
4 0.35367
Differential Equation

87634 \(u \equiv u(x, y)=\sin (y+a x)-(y+a x)^{2}\), then it implies

1 \(u_{x x}=a^{2} \cdot u_{y y}\)
2 \(u_{y y}=a^{2} u_{z x}\)
3 \(u_{x x}=-a^{2} u_{y y}\)
4 \(u_{y y}=-a^{2} u_{x x}\)
Differential Equation

87635 The approximate value of \(\int_{1}^{3} \frac{d x}{2+3 x}\) using
Simpson's rule and dividing the interval \([1,3]\) into two equal parts is

1 \(\frac{1}{3} \log \left(\frac{11}{5}\right)\)
2 \(\frac{107}{110}\)
3 \(\frac{29}{110}\)
4 \(\frac{119}{440}\)
Differential Equation

87645 If \(x^{2}+y^{2}=1\), then

1 \(y\left(y^{\prime \prime}\right)-4\left(y^{\prime}\right)^2+1=0\)
2 \(y\left(y^{\prime \prime}\right)+\left(y^{\prime}\right)^2+1=0\)
3 \(y\left(y^{\prime \prime}\right)-\left(y^{\prime}\right)^2-1=0\)
4 \(y\left(y^{\prime \prime}\right)+2\left(y^{\prime}\right)^2+1=0\)
Differential Equation

87574 The solution of the differential equation \(2 x\left(\frac{d y}{d x}\right)-y=4\) represents a family of

1 Ellipses
2 Parabolas
3 Snaight lines
4 Circles
Differential Equation

87601 The value of \(\int_{0}^{1} x d x\) by Trapezoidal rule taking \(x=4\) is

1 0.34375
2 0.5
3 0.38387
4 0.35367