COMPASSLearning

Talk to us Register Login

CBSE Class 12 · 2011 · Differential EquationsLong Answer

Solve the following differential equation:

(y + 3 x^{2}) \frac{d x}{d y} = x

Answer: $y = 3 x^{2} + C x$

Solution

Invert to get

\frac{d y}{d x} = \frac{y + 3 x ^{2}}{x} = \frac{y}{x} + 3 x

, i.e.

\frac{d y}{d x} - \frac{1}{x} y = 3 x

This is linear with

I.F. = e^{- \int d x / x} = \frac{1}{x}

:

\frac{d}{d x} (\frac{y}{x}) = 3 \Rightarrow \frac{y}{x} = 3 x + C

y = 3 x^{2} + C x

CBSE Class 12 Board · 2011 · Subjective

Practise more: all CBSE board PYQs on Differential Equations →

More board questions on Differential Equations

(a) Find the particular solution of the differential equation
$\frac{d y}{d x} - 2 x y = 3 x^{2} e^{x^{2}}; y (0) = 5$

OR
(b) Solve the following differential equation:
$x^{2} d y + y (x + y) d x = 0$
CBSE 2024View solution →
If $\frac{d}{d x} f (x) = 2 x + \frac{3}{x}$ and $f (1) = 1$ , then $f (x)$ is:
CBSE 2023View solution →
Degree of the differential equation $sin x + cos (\frac{d y}{d x}) = y^{2}$ is:
CBSE 2023View solution →
The integrating factor of the differential equation $(1 - y^{2}) \frac{d x}{d y} + y x = a y, (- 1 < y < 1)$ is:
CBSE 2023View solution →
Find the general solution of the differential equation: $(x y - x^{2}) d y = y^{2} d x$
CBSE 2023View solution →
Find the general solution of the differential equation: $(x^{2} + 1) \frac{d y}{d x} + 2 x y = x^{2} + 4$
CBSE 2023View solution →