The solution of dy dx + y = e^ - x , , ,y(0) = 0, is - Vidyadip

MCQ

The solution of $\frac{{dy}}{{dx}} + y = {e^{ - x}},\,\,y(0) = 0$, is

A
$y = {e^{ - x}}(x - 1)$
B
$y = x{e^x}$
C
$y = x{e^{ - x}} + 1$
✓
$y = x{e^{ - x}}$

✓

Answer

Correct option: D.

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

d
(d) $\frac{{dy}}{{dx}} + y = {e^{ - x}}$; $I.F.$ $ = {e^{\int {dx} }} = {e^x}$

$y{e^x} = \int {{e^{ - x}}.{e^x}dx + c} $ ==> $y{e^x} = x + c$

Since $y(0) = 0$, $c = 0$

Hence, the required solution is $y{e^x} = x$ ==> $y = x{e^{ - x}}$.

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 9. differential equations→9. differential equations — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The total number of local maxima and local minima of the function $f(x)= \begin{cases}(2+x)^3, & -3 < x \leq-1 \\ x^{2 / 3}, & -1 < x <2\end{cases}$

If $\theta$ is the angle between any two vectors $\vec{\text{a}}$ and $\vec{\text{b}},$ then $\big|\vec{\text{a}}.\vec{\text{b}}\big|=\big|\vec{\text{a}}\times\vec{\text{b}}\big|$ when $\theta$ is equal to:

$0$
$\frac{\pi}{4}$
$\frac{\pi}{2}$
$\pi$

Let A = {1, 2, 3}. Then, the number of equivalence relations containing (1, 2) is:

1
2
3
4

The number of bijective functions from set $A$ to itself when $A$ contains 106 elements is

The function $f(x)=2 x+3(x)^{\frac{2}{3}}, x \in \mathbb{R}$, has

Let X be a discrete random variable. Then the variance of X is:

E(X²)
E(X²) + (E(X))²
E(X²) - (E(X))²
$\sqrt{\text{E}(\text{X}^2)-(\text{E}(\text{X}))^2}$

The vector having initial and terminal points as $(2,5,0)$ and $(-3,7,4)$ respectively is

In equation $3\text{x}-\text{y}\geq3$ and 4x - 4y > 4.

If $\vec{a}=\hat{i}+\hat{j}-\hat{k}$ then the value of $|\vec{a}|^2$ will be -

Let three points $A(2,3,4), B(3,4,2)$ and $C(4,2,3)$ in space are given. A point $D$ in space is such that it is at a distance of $\sqrt 6$ units from $3$ given points. Then volume of tetrahedron $ABCD$ is -