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Solve: [(x+1)y/x+siny]dx+[x+log(e)x+xco...

Solve: `[(x+1)y/x+siny]dx+[x+log_(e)x+xcosy]dy=0`

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Verified by Experts

We can rewrite the given equation as
`(ydx+xdy)+(y/xdx+log_(e)xdy)+(sinydx+xcosydy)=0`
`rArr d(xy)=(yd(log_(e)x)+log_(e)xdy)+(sinydx+xd(siny))=0`
`rArr d(xy)+d(ylog_(e)x) + d(xsiny)=0`
Integrating both the sides, we get
`xy+ylog_(e)x+xsiny=C`
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CENGAGE-DIFFERENTIAL EQUATIONS-Question Bank
  1. Solve: [(x+1)y/x+siny]dx+[x+log(e)x+xcosy]dy=0

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  2. A function is continuous and differentiable on R0 satisfying x f^(prim...

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  3. A curve y=f(x) is passing through (0,0). If the slope-of the curve at ...

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  4. If y=f(x) satisfies the differential equation (1+x^2) f^(prime)(x)=x(1...

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  5. If y(x) is solution of (x+1) (d y)/(d x)-x y=1, y(0)=-1, then y(-6/5) ...

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  6. Let perpendicular distance of any variable tangent on the curve C fro...

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  7. The number of straight lines which satisfies the differential equation...

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  8. The real valuc of m for which the 'substitution, y=u^m will transform ...

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  9. A function y=f(x) satisfies the differential equation (d y)/(d x)+x^2 ...

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  10. If the differential equation representing the family of curves y=C1 co...

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  11. The family of integral curves of the differential equation (d y)/(d x)...

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  12. If ' e' denotes tho cccentricity of the hyperbola, satisfying the dif...

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  13. A carve y=f(x) passes through O(0,0) and slope of tangent line at any ...

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  14. If y=x sin (ln x) is the solution of x^2((d y)/(d x))^2-(lambda-2) x ...

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  15. Let y=f(x) be drawn with f(0)=2 and for each real number ' a ' the lin...

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  16. If tangent to the curve x y=x^2+1 at (alpha, beta) is normal to the cu...

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  17. If y=y(x) and it follows the relation 4 x e^v=y+5 sin ^2 x then y^prim...

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  18. Given y(0)=2000 and (d y)/(d x)=32000-20 y^2, then find the value of u...

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  19. If the differential equation corresponding to the family of curves, y=...

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  20. A curve in the first quadrant is such that the area of the triangle fo...

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  21. Number of values of m in N for which y=e^(mx) is a solution of the di...

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