Solve the following differential equations : d y+(2 y) d x=8 d x - Vidyadip

Question

Solve the following differential equations : $d y+(2 y) d x=8 d x$

✓

Answer

$dy +(2 y ) dx =8 dx$
$\therefore \frac{d y}{d x}+2 y =8$
This is the linear differential equation of the form
$ \frac{d y}{d x}+P y=Q, \text { where } P=2, Q=8$
$\therefore \text { I.F. } =e^{\int P d x}=e^{2 \int d x}=e^{2 x}$
$ \therefore \text { the solution } f(1) \text { is given by }$
$ y \cdot \text { (I.F.) }=\int Q(\text { I.F.) } d x+c$
$ \therefore y e^{2 x}=\int 8 e^{2 x} d x+c$
$ \quad=8\left(\frac{e^{2 x}}{2}\right)+c$
$ \therefore y e^{2 x}=4 e^{2 x}+c$
This is the general solution.

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.(2 Marks)" from Differential Equation and Applications (p-1)→Differential Equation and Applications (p-1) — all question types→Maths (commerce) STD 12 Commerce / Arts question papers→Maharashtra Board STD 12 Commerce / Arts question papers→Maharashtra Board question paper generator→

Similar questions

Priya gets a salary of $\text{₹} 15,000$ per month and a commission of $8\%$ on sales over $\text{₹} 50,000.$ If she gets $\text{₹} 17,400$ in a certain month. Find the sales made by her in that month.

Evalute : $\int x^3 e^{x^2} d x$

Find y if the cost of living index is 200

Group	Food	Clothing	Fuel & Lighting	House Rent	Miscellaneous
I	180	120	160	300	200
W	4	5	3	y	2

Construct the truth table for each of the following statement patterns : (p ∨ r) → ~(q ∧ r)

Evalute : $\int \sqrt{x^2-8 x+7} d x$

(i) If for a bivariate data $b_{y x}=-1.2$ and $b_{x y}=-0.3$ then find $r$.
(ii) From the two regression equations $\mathrm{y}=4 \mathrm{x}-5$ and $3 \mathrm{x}=2 \mathrm{y}+5$, find $\bar{x}$ and $\bar{y}$.

If Laspeyre’s Price Index Number is four times Paasche’s Price Index Number, then find the relation between Dorbish-Bowley’s and Fisher’s Price Index Numbers.

Find the probability distribution of the number of successes in two tosses of a die if successes are defined as getting a number greater than 4.

A factory building is insured for $\left(\frac{5}{6}\right)^{\text {th }}$ of its value at a rate of premium of $2.50 \%$. If the agent is paid a commission of ₹ $2,812.50$, which is $7.5 \%$ of the premium, find the value of the building.

70% of the member’s favour and 30% oppose a proposal in a meeting. The random variable X takes the value 0 if a member opposes the proposal and the value 1 if a member is in favour. Find E(X) and V(X).