Solve the following differential equations: dy+(x+1)(y+1)dx=0 - Vidyadip

Question

Solve the following differential equations:
$\text{dy}+(\text{x}+1)(\text{y}+1)\text{dx}=0$

✓

Answer

$\text{dy}+(\text{x}+1)(\text{y}+1)\text{dx}=0$
$\text{dy}=-(\text{x}+1)(\text{y}+1)\text{dx}$
$\int\frac{\text{dy}}{\text{y}+1}=-\int(\text{x}+1)\text{dx}$
$\log|\text{y}+1|=-\frac{\text{x}^2}{2}-\text{x}+\text{C}$
$\log|\text{y}+1|+\frac{\text{x}^2}{2}+\text{x = C}$

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 "3 Marks" from DIFFERENTIAL EQUATIONS→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

If f: N $\to$ N is defined by f(n) = $\left\{ \begin{array} { l } { \frac { n + 1 } { 2 } , \text { if } n \text { is odd } } \\ { \frac { n } { 2 } , \text { if } n \text { is even } } \end{array} \right.$for all n $ \in$ N. State whether the function f is bijective. Justify your answer.

Find the set of values of 'a' for which $\text{f}(\text{x})=\text{x}+\cos\text{x}+\text{ax}+\text{b}$ is increasing on R.

Evaluate the following integrals:
$\int\frac{5\text{x}^4+12\text{x}^3+7\text{x}^2}{\text{x}^2+\text{x}}\text{dx}$

Evaluate the following integrals:
$\int\sec^6\text{x }\tan\text{x}\text{ dx}$

Evaluate the following intregals:
$\int\frac{1}{\cos\text{x}(\sin\text{x}+2\cos\text{x})}\ \text{dx}$

Differentiate w.r.t. x the function in Exercise:
$\frac{\cos^{-1}\frac{\text{x}}{2}}{\sqrt{2\text{x}+7}},-2<\text{x}<2$

If $\vec{\text{a}},\vec{\text{b}}$ are two vectors such that $\big|\vec{\text{a}}+\vec{\text{b}}\big|=\big|\vec{\text{b}}\big|,$ then prove that $\vec{\text{a}}+2\vec{\text{b}}$ is perpendicular to $\vec{\text{a}}.$

Discuss the applicability of the Rolle's theorem for the following function on the indicated interval
$\text{f}(\text{x})=[\text{x}]\text{ for }-1\leq\text{x}\leq1,$ where [x] denotes the greatest integer not exceeding x.

Find the approximate change in the value V of a cube of side x metres caused by increasing the side by 1%.

Solve the following differential equations:

$\frac{\text{dr}}{\text{dt}}=-\text{rt, r}(0)=\text{r}_{0}$