y + x^2 = dy dx has the solution - Vidyadip

MCQ

$y + {x^2} = \frac{{dy}}{{dx}}$ has the solution

✓
$y + {x^2} + 2x + 2 = c{e^x}$
B
$y + x + {x^2} + 2 = c{e^{2x}}$
C
$y + x + 2{x^2} + 2 = c{e^x}$
D
${y^2} + x + {x^2} + 2 = c{e^x}$

✓

Answer

Correct option: A.

$y + {x^2} + 2x + 2 = c{e^x}$

a
(a) $y + {x^2} = \frac{{dy}}{{dx}}$ ==> $\frac{{dy}}{{dx}} - y = {x^2}$

This is the linear differential equation in $y$, where $P = - 1,\,Q = {x^2}$

$I.F.$ $ = {e^{\int {P.dx} }}$$ = {e^{\int { - dx} }} = {e^{ - x}}$

Hence solution, $y.\,({\rm{I}}{\rm{.F}}). = \int {Q.({\rm{I}}{\rm{.F}})\,dx + c} $

==> $y{e^{ - x}} = - {x^2}{e^{ - x}} - 2x{e^{ - x}} - 2{e^{ - x}} + c$

==> $y + {x^2} + 2x + 2 = c{e^x}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 9. differential equations→STD 12 - 9. differential equations — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

$\int\text{x}^2\sin\text{x}^3\text{dx}=$

In a certain town, $40\%$ persons have brown hair, $25\%$ have brown eyes, and $15\%$ have both. If a person selected at random has brown hair, the chance that a person selected at random with brown hair is with brown eyes

If $\text{f(x)}=\begin{cases}\frac{\log(1+\text{ax})-\log(1-\text{bx})}{\text{x}},&\text{x}\neq0\\\text{k},&\text{x}=0\end{cases}$ and $f(x)$ is continous at $x = 0,$ then the value of $k$ is :

Can $\frac{1}{\sqrt{3}},\frac{2}{\sqrt{3}},\frac{-2}{\sqrt{3}}$ be the direction cosines of any directed line:

If $\text{A B C D}$ is a parallelogram and $A C$ and $B D$ are its diagonals, then $\overrightarrow{A C}+\overrightarrow{B D}$ is:

Let $X$ be a non-empty set and let $P(X)$ denote the collection of all subsets of $X$. Define $f: X \times P(X) \rightarrow R$ by $f(x, A)=\left\{\begin{array}{ll}1, & \text { if } x \in A \\ 0, & \text { if } x \notin A^*\end{array}\right.$ Then, $f(x, A \cup B)$ equals

A purse contains $4$ copper coins and $3$ silver coins. A second purse contains $6$ copper coins and $4$ silver coins. A purse is chosen randomly and a coin is taken out of it. What is the probability that it is a copper coin?

Evaluate: $\int \frac{10 x^9+10^x \log _e 10}{10^x+x^{10}} d x$

If $\tan^{-1}(\text{x}-1)+\tan^{-1}\text{x}+\tan^{-1}(\text{x}+1)=\tan^{-1}3\text{x},$ then the values of $x$ are:

The area bounded by a curve, the axis of co-ordinates $\&$ the ordinate of some point of the curve is equal to the length of the corresponding arc of the curve. If the curve passes through the point $P (0, 1)$ then the equation of this curve can be