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The solution of the differential equatio...

The solution of the differential equation `y^(prime prime prime)-8y^(prime prime)=0,` where `y(0)=1/8,y^(prime)(0)=0,y^(prime prime)(0)=1` , is

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`y^(''')/y^('')=8` or `logy^('')=8x+c`
When `x=0, y^('')=1` or `log1=0`. Thus, c=0.
`therefore y^(')=e^(8x)`
Integrating again, we get
`y^(')=e^(8x)/8+lambda`
When `x=0, y^(')(0)=0`
`therefore lambda=-1/8`
`therefore y^(')=e^(8x)/8-1/8`.
Integrate again. Then,
`y=e^(8x)/64-x/8+k`
Also, when `x=0,y=1/8`. Thus, `k=7/64`.
`therefore y=1/8(e^(8x)/8-x+7/8)`
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CENGAGE-DIFFERENTIAL EQUATIONS-Exercise (Single)
  1. The solution of the differential equation (d^2y)/(dx^2)=sin3x+e^x+x^2 ...

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  2. Find the solution of the differential equation y^(')y^(''')=3(y^(''))^...

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  3. The solution of the differential equation y^(prime prime prime)-8y^(pr...

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  4. The slope of the tangent at (x , y) to a curve passing through (1,p...

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  5. Solve x((dy)/(dx))=y(logy-logx+1)

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  6. The solution of differential equation x y^(prime)=x((y^2)/(x^2)+(f((y^...

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  7. The solution of (x^2+x y)dy=(x^2+y^2)dx is (a) ( b ) (c)logx=log(( d ...

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  8. The solution of (y+x+5)dy=(y-x+1)dx is

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  9. The slope of the tangent at (x , y) to a curve passing through a po...

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  10. Solution of the differential equation ydx-xdy+xsqrt(xy)dy=0 is

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  11. The solution of (x^2dy)/(dx)-x y=1+cosy/x is (a) ( b ) (c)tan(( d ) (...

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  12. The solution of the differential equation 2x^2y(dy)/(dx)=tan(x^2y^2)-2...

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  13. Solution of the differential equation {1/x-(y^2)/((x-y)^2)}dx+{(x^2)/(...

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  14. The solution of differential equation (2y+x y^3)dx+(x+x^2y^2)dy=0 is (...

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  15. Find the solution of y e^(-x/y)dx-(x e^((-x/y))+y^3)dy=0 is

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  16. Find the curve satisfying the equation (dy)/(dx)=(y(x+y^3))/(x(y^3-x))...

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  17. Find the solution of differential equation (x+y(dy)/(dx))/(y-x(dy)/(...

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  18. The solution of the differential equation (dy)/(dx)=(3x^2y^4+2x y)/(x^...

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  19. The solution of the differential equation {1+xsqrt((x^2+y^2))}dx+{sqrt...

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  20. The solution of differential equation (y(2x^4+y)dy)/(dx)=(1-4x y^2)x^2...

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