The solution of x d y d x +y=e^x is - Vidyadip

Question

The solution of $x \frac{d y}{d x}+y=e^x$ is

✓

Answer

$\text { (a) : } x \frac{d y}{d x}+y=e^x$
$\frac{d y}{d x}+\frac{y}{x}=\frac{e^x}{x}$
It is a linear differential equation with
$\text { I.F. }=e^{\int \frac{1}{x} d x}=e^{\log x}=x$
Now, solution is $y \cdot x=\int \frac{e^x}{x} \cdot x d x+c$
$\Rightarrow y x=e^x+c \Rightarrow y=\frac{e^x}{x}+\frac{c}{x}$

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 Differential Equations→Differential Equations — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If A and B are symmetric matrices of the same order, then:

AB is a symmetric matrix.
A - Bis askew-symmetric matrix.
AB + BA is a symmetric matrix.
AB - BA is a symmetric matrix.

If $\begin{vmatrix}\text{a}&\text{p}&\text{x}\\\text{b}&\text{q}&\text{y}\\\text{c}&\text{r}&\text{z}\end{vmatrix}=16,$ then the value of $\begin{vmatrix}\text{p}+\text{x}&\text{a}+\text{x}&\text{a}+\text{p}\\\text{q}+\text{y}&\text{b}+\text{y}&\text{b}+\text{q}\\\text{r}+\text{z}&\text{c}+\text{z}&\text{c}+\text{r}\end{vmatrix}$ is:

4
8
16
32

For what value of $a, f(x)=-x^3+4 a x^2+2 x-5$ is decreasing $\forall x$ ?

If the function $\text{f(x)}=\frac{2\text{x}-\sin^{-1}\text{x}}{2\text{x}+\tan^{-1}\text{x}}$ is continuous at each point of its domain, then the value of f(0) is:

$2$
$\frac{1}{3}$
$-\frac{1}{3}$
$\frac{2}{3}$

The area bounded by the curve $y = x^2 + 4x + 5,$ the axes of coordinates and minimum ordinate is$:$

The order of the differential equation whose general solution is given by
$
y=\left(C_1+C_2\right) \cos \left(x+C_3\right)-C_4 e^{x+C_5}
$
where $C_1, C_2, C_3, C_4, C_5$ are arbitrary constants, is

$\int_0^{\pi / 4} \tan ^2 x d x$ is equal to :

If a function $\text{f}:(2,\infty)\rightarrow\ \text{B}$ defined by $f(x) = x^2 - 4x + 5$ is a bijection, then $B =$

If $\big[2\vec{\text{a}}+4\vec{\text{b}}\vec{\text{c}}\vec{\text{d}}\big]=\lambda\big[\vec{\text{a}}\vec{\text{c}}\vec{\text{d}}\big]+\mu\big[\vec{\text{b}}\vec{\text{c}}\vec{\text{d}}\big],$ then $\lambda+\mu=$

6
-6
10
8

If $\text{y}=\log\Big(\frac{1-\text{x}^2}{1+\text{x}^2}\Big),$ then $\frac{\text{dy}}{\text{dx}}=$

$\frac{4\text{x}^3}{1-\text{x}^4}$
$-\frac{4\text{x}}{1-\text{x}^4}$
$\frac{1}{4-\text{x}^4}$
$-\frac{4\text{x}^3}{1-\text{x}^4}$