Solve the differential equation d y d x +y=e^ -x - Vidyadip

Question

Solve the differential equation $\frac{d y}{d x}+y=e^{-x}$

✓

Answer

$\frac{d y}{d x}+y=e^{-x}$
The given equation is of the form
$\frac{d y}{d x}+p y=Q$
where, $P = 1$ and $Q = e^{-x}$
$\therefore$ I.F. $=e \int^{p d x}=e \int^{1 . d x}=e^x$
$\therefore $ Solution of the given equation is
$ y(I . F .)=\int Q(I . F .) d x+c$
$ \therefore y e^x=\int e^{-x} e^x d x+c$
$ \therefore y e^x=\int 1 d x+c$
$ \therefore ye ^{ x }= x + c $

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 "Solve the Following Question.(3 Marks)" from Differential Equations→Differential Equations — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Check the commutativity and associativity of the following binary operations:
'*' on Z defined by a * b = a + b - ab for all a, b ∈ Z.

Find $\frac{d y}{d x}$ if : $x=\sqrt{1-t^2}, y=\sin ^{-1} t$

Using determinants, find the value of k so that the points $(k, 2 - 2k), (-k + 1, 2k)$ and $(-4 - k, 6 - 2k)$ may be collinear.

Solve the differential equation, $d r+(2 r \cot \theta+\sin 2 \theta) d \theta=0$.

Find the acute angle between lines x = y, z = 0 and x = 0, z = 0.

$\int\frac{1-\cos\text{x}}{1+\cos\text{x}}\text{dx}$

Find $\frac{d y}{d x}$ if

$x=\cos ^{-1}\left(4 t^3-3 t\right), y=\tan ^{-1}\left(\frac{\sqrt{1-t^2}}{t}\right)$

Prove that the sum of the three vectors determined by the medians of a triangle directed from the vertices is zero.

Find the approximate value of $\tan ^{-1}(0.99)$, Given that $\pi \doteqdot 3.1416$.

Find a unit vector perpendicular to both the vectors $4\hat{\text{i}}-\hat{\text{j}}+3\hat{\text{k}}$ and $-2\hat{\text{i}}+\hat{\text{j}}-2\hat{\text{k}.}$