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Solve: 1.(x+1)(dy)/(dx)=2x y 2.cosx...

Solve: 1.`(x+1)(dy)/(dx)=2x y` 2.`cosx(1+cosy)dx-s in y(1+sinx)dy=0`

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Verified by Experts

Given
`(x+1)(dy)/(dx)=2x y`
`I=(x+1)(dy)/(dx)=2x y`
`I=(dy)/y=2x/(x+1)`
`I=(dy)/y=2[(x+1-1)/(x+1)]`
`I=int(dy)/y=2int[(x+1-1)/(x+1)]`
On integration we get
`log|y|=2[x-log|x+1|]+c`
...
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RD SHARMA-DIFFERENTIAL EQUATION-Solved Examples And Exercises
  1. Solve the initial value problem e^((dy//dx))=x+1; y(0)=5.

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  2. Solve the following initial value problems: (22-26) x(x^2-1)("dy")/("...

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  3. Solve: 1.(x+1)(dy)/(dx)=2x y 2.cosx(1+cosy)dx-s in y(1+sinx)dy=0

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  4. Solve the following differential equations: y-x(dy)/(dx)=a(y^2+(dy)...

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  5. Solve: log((dy)/(dx))=a x+b y

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  6. Solve the initial value problem y^(prime)=ycot2x ,y(pi/4)=2.

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  7. if a,b are two positive numbers such that f(a+x)=b+[b^3+1-3b^2f(x)+3b...

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  8. Solve the initial value problem: dy=e^(2x+y)dx ,y(0)=0.

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  9. Solve the initial value problem: x(xdy+ydx)=ydx ,y(1)=1.

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  10. Solve: (dy)/(dx)=ysin2x it being given that y(0)=1.

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  11. Solve the initial value problem: (xdy+ydx)=xy dx ,y(1)=1.

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  12. Find the equation of the curve passing through origin if the slope ...

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  13. Find the equation of the curve passing through the point (1,0) if t...

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  14. Find the equation of the curve passing through the point (-2,3) giv...

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  15. Find the equation of the curve passing through the point (1,1) whos...

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  16. Solve the following differential equation : xcosy\ dy=(x e^xlogx+e^x)...

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  17. Solve the following differential equations: xcos^2y \ dx=ycos^2x \ dy

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  18. Experiments show that the rate of inversion of cane sugar in dilute so...

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  19. In a culture, the bacteria count is 1,00,000. The number is increas...

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  20. A bank pays interest by continuous compounding, that is ,by treatin...

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