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Hard Ordinary differential equations, their order and degree MCQs for JEE

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Part of Differential Equations in JEE Main Mathematics.

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Q1MathsUnit 9: Differential Equations
The order, degree of the differential equation satisfying the relation 1+x2+1+y2=λ(x1+y2)\sqrt{1+x^{2}}+\sqrt{1+y^{2}}=\lambda(x \sqrt{1+y^{2}}) y1+x2)\left.y \sqrt{1}+x^{2}\right) is
Q2MathsUnit 9: Differential Equations
The family of curves represented by dy1dx=x2+x+1y2+y+1\frac{d y_{1}}{d x}=\frac{x^{2}+x+1}{y^{2}+y+1} and the family represented by dy2dx+y2+y+1x2+x+1=0\frac{\boldsymbol{d} \boldsymbol{y}_{2}}{\boldsymbol{d} \boldsymbol{x}}+\frac{\boldsymbol{y}^{2}+\boldsymbol{y}+\mathbf{1}}{\boldsymbol{x}^{2}+\boldsymbol{x}+\mathbf{1}}=\mathbf{0}
Q3MathsUnit 9: Differential Equations
The order and degree of the differential equation, (d2ydx2)3=sin⁡y+3x\left(\frac{d^{2} y}{d x^{2}}\right)^{3}=\sin y+3 x \quad are
Q4MathsUnit 9: Differential Equations
The order and degree of the differential equation. (d2ydx2)3+(dydx)=∫ydx\left(\frac{d^{2} y}{d x^{2}}\right)^{3}+\left(\frac{d y}{d x}\right)=\int y d x are respectively.
Q5MathsUnit 9: Differential Equations
Find the order and degree of (1+(1+ y′)1/2=y′′\left.\boldsymbol{y}^{\prime}\right)^{1 / 2}=\boldsymbol{y}^{\prime \prime}
Q6MathsUnit 9: Differential Equations
Assertion The order of the differential equation, of which xy=cex+be−x+x2\boldsymbol{x} \boldsymbol{y}=\boldsymbol{c} \boldsymbol{e}^{\boldsymbol{x}}+\boldsymbol{b} \boldsymbol{e}^{-\boldsymbol{x}}+\boldsymbol{x}^{\boldsymbol{2}} is a solution, is 2 Reason The differential equation is xd2ydx2+x \frac{d^{2} y}{d x^{2}}+ 2dydx−xy+x2−2=02 \frac{d y}{d x}-x y+x^{2}-2=0
Q7MathsUnit 9: Differential Equations
The differential equation corresponding to xy=c2,x y=c^{2}, where cc is an arbitrary constant, is:
Q8MathsUnit 9: Differential Equations
Order and degree of (x2+2x)y22+(x2−2)y13−2(x+\left(x^{2}+2 x\right) y_{2}^{2}+\left(x^{2}-2\right) y_{1}^{3}-2(x+ 3)y=0\mathbf{3}) \boldsymbol{y}=\mathbf{0} are:

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