Differential Equation

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

Click on each question to see answer & solution.

Question No: #31

Solve: `\frac{dy}{dx}=1+e^{2x-y}` ; given `y(2)=2`
Ans: `e^{2x}-e^y=(e^2-1)e^x`
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Question No: #32

The general solution of differential equation `\frac{dy}{dx}+x^2=x^2e^3y` is -- (i) `1-e^3y=ce^{x^3}`, (ii) `1-e^3y=ce^{-x^3}`, (iii) `(1-e^{-3}y)^2=c^2e^{2x^3}`, (iv) None of these.

Question No: #33

Find the integrating factor of `x\frac{dy}{dx}-y=x\logx`

Question No: #34

Find the Integrating Factor of `(1+y^2)dx=(\tan^{-1}y-x)dy`

Question No: #35

The integrating factor of `x(x-1)\frac{dy}{dx}-y=x^2(x-1)^2` is -- (i) `\frac{x-1}{x}`, (ii) `\frac{x}{x-1}`, (iii) `\frac{1-x}{x}`, (iv) `\frac{x}{1-x}`

Question No: #36

The Integrating Factor of `(x+y+1)\frac{dy}{dx}=1` is -- (i) `e^x`, (ii) `e^{-x}`, (iii) `e^y`, (iv) `e^{-y}`

Question No: #37

The integrating factor of `\frac{dx}{dy}+x/y=\frac{1}{y^2}` is -- (i) `logy`, (ii) `e^y`, (iii) `y`, (iv) `1/y`

Question No: #38

Find particular solution of `(x-y)(dx+dy)=dx-dy` where it is given that `y=-1` when `x=0`

Question No: #39

Solve: `(x+y)(dx-dy)=dx+dy`

Question No: #40

Solve: `(x\cosx)\frac{dy}{dx}+(x\sinx+\cosx)y=1`