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Ordinary differential equations, their order and degree Revision for JEE

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Revise Ordinary differential equations, their order and degree by covering every subtopic once, drilling formulas, then solving 8+ timed MCQs with full solutions.

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Revision checklist

  1. 1.Core idea: Ordinary differential equations, their order and degree
  2. 2.Relates to other subtopics in Differential Equations
  3. 3.Order and degree identification
  4. 4.Separation of variables
  5. 5.Master Ordinary differential equations, their order and degree definitions and standard results
  6. 6.Solve 20 timed MCQs for Ordinary differential equations, their order and degree

Syllabus context

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
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
Q6MathsUnit 9: Differential Equations
The differential equation corresponding to xy=c2,x y=c^{2}, where cc is an arbitrary constant, is:
Q7MathsUnit 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:
Q8MathsUnit 9: Differential Equations
Consider the following statements: 1. The general solution of dydx=f(x)+\frac{d y}{d x}=f(x)+ xx is of the form y=g(x)+c,y=g(x)+c, where cc is an arbitrary constant. 2. The degree of (dydx)2=f(x)\left(\frac{d y}{d x}\right)^{2}=f(x) is 2 Which of the above statements is/are correct?

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Follow the checklist on this page, revise formulas daily, and attempt mixed MCQs every 2–3 days.

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