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Differential Equations formula sheet

Every formula in the Differential Equations chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 22 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that formula, and "last" is the latest year one appeared. ★ marks formulas asked 8 or more times.

Order, degree and formation

Order and degree
1× asked, last 2021
order=highest derivativedegree=its power (polynomial in derivatives)\begin{aligned}&\text{order}=\text{highest derivative}\\&\text{degree}=\text{its power (polynomial in derivatives)}\end{aligned}
No degree if a derivative sits inside sin, exp or log. Clear roots first: y=xy′+1+y′2y=xy^{\prime}+\sqrt{1+y^{\prime2}} has degree 2.
Forming a DE
6× asked, last 2024
n arbitrary constants⇒differentiate n times, eliminaten\text{ arbitrary constants}\Rightarrow\text{differentiate }n\text{ times, eliminate}
Order nn. Count independent constants: aex+b=Aexae^{x+b}=Ae^x has one. A given radius is not a constant.

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Practise Differential Equations

20 more formulas in 4 topics

Variable separable and reducible forms, Homogeneous equations, Linear equations and Bernoulli form and Initial values and applications. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Variable separable and reducible forms

  • Variable separable28×
  • Substitution t = ax + by + c8×
  • Exact differentials17×
  • Exact differentials: logs, tan⁻¹

Homogeneous equations

  • Put y = vx16×
  • Put x = vy4×
  • Shift the origin3×
  • Power substitutions6×

Linear equations and Bernoulli form

  • Linear equation in y40×
  • Integrating factors to know24×
  • Constant coefficients10×
  • Linear in x9×
  • Make it linear: t = f(y)12×
  • Bernoulli equation5×

Initial values and applications

  • Initial-value problems23×
  • Using the solution25×
  • Growth, decay and cooling5×
  • Curves from a slope condition11×
  • Integral equations12×
  • Second-order forms4×

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About 205 past JEE Main questions from this chapter, with instant answer checking and step-by-step solutions where available. Free, and you can start without signing up.

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Version 1, October 2026. Free to share for study, as it is. Please don't sell it or remove the PrepWiser name.

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