Differential Equation

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #111

Solve: `(x+1)\frac{dy}{dx}-y=e^{3x}(x+1)^2`
Ans: `\frac{y}{1+x} = \frac{e^{3x}}{3} + c`
SEE SOLUTION

Question No: #112

Solve: `\frac{dy}{dx}+\frac{y}{\log_ex}=\frac{2}{x}`

Question No: #113

Solve: `\frac{dy}{dx}+\frac{y}{x\log_ex}=2/x`
Ans: `ylogx = (logx)^2 + c`
SEE SOLUTION

Question No: #114

Solve: `\cos^2x\frac{dy}{dx}+y=\tanx` ; where `0\lex\le\frac{\pi}{2}`
Ans: `y = tanx -1 +c e^{-tanx}`
SEE SOLUTION

Question No: #115

Solve: `\frac{dy}{dx}+y\secx=\tanx` ; where `0\le\x\le\frac{\pi}{2}`
Ans: `y\ (secx+tanx) = secx + tanx - x + c`
SEE SOLUTION

Question No: #116

Solve: `\sinx\frac{dy}{dx}+3y=\cosx`

Question No: #117

Solve: `\frac{dy}{dx}+y\cotx=2\cosx`
Ans: `y\ sinx = - \frac{cos2x}{2} + c`
SEE SOLUTION

Question No: #118

Solve: `\frac{dy}{dx}-3y\cotx=\sin2x`, given `y=2` when `x=\pi/2`

Question No: #119

Solve: `\frac{dy}{dx}+y\cotx=2x+x^2\cotx` ; where `y(0)=0`
Ans: `y sinx = x^2 sinx`
SEE SOLUTION

Question No: #120

Solve: `\frac{dy}{dx}=-\frac{x+y\cosx}{1+\sinx}`
Ans: `y\ (1+sinx) +x^2/2 = c`
SEE SOLUTION