Calculus

Differential Equations

Easy

The general solution of the differential equation $\frac{dy}{dx} = e^{x+y}$ , is :

$e^x + e^y = c$

$y = e^{x+y} + c$

$e^x + e^{-y} = c$

$e^x - e^{-y} = c$

✅ Correct Option: 3

$\frac{dy}{dx} = e^x \cdot e^y$ . Separate variables: $e^{-y} \, dy = e^x \, dx$ .

Integrate: $-e^{-y} = e^x + c_1$ .

Rearranging: $e^x + e^{-y} = c$ (where $c = -c_1$ ).

2023: 15 June Shift 2

The differential equation whose solution is $Ax^2 + By^2 = 1$ where A and B are arbitrary constant is of :

(A) first order and first degree

(B) second order and first degree

(D) second order

Choose the correct answer from the options given below :

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The differential equation representing family of circles with centre at origin and radius r units is-

The general solution of the differential equation dydx=ex+y\frac{dy}{dx} = e^{x+y}dxdy​=ex+y, is :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The general solution of the differential equation $\frac{dy}{dx} = e^{x+y}$ , is :