Differential Equation

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

Click on each question to see answer & solution.

Question No: #51

Solve: `(e^x+1)y\ dy-(y^2+1)e^xdx=0` ; given `y(0)=0`

Question No: #52

Solve: `(1+e^{2x})dy+e^x(1+y^2)dx=0` ; given `y(0)=1`
Ans: `tan^{-1}y = -1/2 log(1+e^{2x})+\frac{\pi}{4} + 1/2 log2`
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Question No: #53

Solve: `y\ dx-x\ dy=xy\ dx`, when `x=1`, `y=1`
Ans: `log |x/y| = x - 1`
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Question No: #54

Solve: `x\ dy-y\ dx=(x^2+y^2)dx`
Ans: `tan^{-1}(y/x) = x+c`
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Question No: #55

Solve: `xdx+ydy+\frac{xdy-ydx}{x^2+y^2}=0` given `y=1` when `x=1`
Ans: `tan^{-1}(y/x) = - (\frac{x^2+y^2}{2}) + \frac{\pi}{4} + 1`
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Question No: #56

Solve: `x^2(x\ dx+y\ dy)+2y(x\ dy-y\ dx)=0`

Question No: #57

The general solution of differential equation `ydx+xdy=xy(dy-dx)` is -- (i) `\ln(cxy)=x-y`, (ii) `\ln(xy)=cxy`, (iii) `\ln(cxy)=y-x`, (iv) None of these.
Ans: (i) `\ln(cxy)=x-y`
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Question No: #58

The general solution of differential equation `y^2(x\ dy+y\ dx)+(x\ dy-y\ dx)=0` is -- (i) `xy=x/y+c`, (ii) `x+y=xy+c`, (iii) `log|x+y|=cx`, (iv) `log|x/y|=x/y+c`
Ans: (i) `xy=x/y+c`
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Question No: #59

General solution of `x^2(x\ dy+y\ dx)+(x\ dy-y\ dx)=0` is -- (i) `xy+y/x=c`, (ii) `xy-y/x=c`, (iii) `xy+x/y=c`, (iv) `x/y-xy=c`
Ans: (i) `xy+y/x=c`
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Question No: #60

Solve: `xdy-ydx=2\sqrt{y^2-x^2}dx`
Ans: `- sin^{-1}(x/y) = 2x+c`
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