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The general solution of the differential...

The general solution of the differential equation, `y^(prime)+yvarphi^(prime)(x)-varphi^(prime)(x) varphi(x)=0`, where `varphi(x)` is a known function, is

A

`y=ce^(-phi(x))+phi(x)-1`

B

`y=ce^(+phi(x))+phi(x)-1`

C

`y=ce^(-phi(x))-phi(x)+1`

D

`y=ce^(-phi(x))+phi(x)+1`

Text Solution

Verified by Experts

The correct Answer is:
A
`therefore (dy)/(dx) +y/(xlog_(e)x)=2/x`
`therefore` I.F. `=e^(phi(x))phi(x)phi^(')(x)dx`
`=inte^(t)tdt`, where `phi(x)=t`
`=te^(t)-e^(t)+c`
`=phi(x)e^(phi(x))+phi(x)-1`
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CENGAGE-DIFFERENTIAL EQUATIONS-Exercise (Single)
  1. The solution of the differential equation (xcoty+logcosx)dy+(logsiny-y...

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  2. If =(e^y-x)^(-1), where y(0)=0 , then y is expressed explicitly as ...

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  3. The general solution of the differential equation, y^(prime)+yvarphi^(...

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  4. The integrating factor of the differential equation (dy)/(dx)(x(log)x)...

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  5. The solution of the differential equation x(x^2+1)((dy)/(dx))=y(1-x^2)...

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  6. Integrating factor of the differential equation cosx(dy)/(dx)+ysinx=1 ...

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  7. Solution of the equation cos^2x(dy/dx)-(tan2x)y=cos^4x, when y(pi/6)=(...

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  8. If integrating factor of x(1-x^2)dy+(2x^2y-y-a x^3)dx=0 is e^(intp dx...

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  9. A function y=f(x) satisfies (x+1)f^(prime)(x)-2(x^2+x)f(x)=(e^x^2)/((x...

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  10. The general solution of the equation (dy)/(dx)=1+x y is (a) ( b ) (...

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  11. The solution of the differential equation (x+2y^3)(dy)/(dx)=y is

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  12. The solution of the differential equation x^2(dy)/(dx)cos(1/x)-ysin(1/...

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  13. The solution of (dy)/(dx)=(x^2+y^2+1)/(2x y) satisfying y(1)=1 is

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  14. The solution of the differential equation (dy)/(dx)=1/(x y[x^2siny^2+1...

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  15. Find the equation of a curve passing through (2,7/2) and having grad...

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  16. Which of the following is not the differential equation of family o...

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  17. Tangent to a curve intercepts the y-axis at a point Pdot A line ...

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  18. Orthogonal trajectories of family of the curve x^(2/3)+y^(2/3)=a^((2/3...

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  19. The curve in the first quadrant for which the normal at any point (...

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  20. The equation of the curve which is such that the portion of the axi...

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