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Makovka662 [10]
3 years ago
5

Solution for dy/dx+xsin 2y=x^3 cos^2y

Mathematics
1 answer:
IrinaVladis [17]3 years ago
3 0
Start by putting the dy/dx by itself
\frac{dy}{dx}+xsin2y=x^3 cos^2y \\ \frac{dy}{dx}=x^3 cos^2y-xsin2y
then multiply both sides by dx
dy=(x^3cos^2y-xsin2y)dx
which you can now integrate both sides with respect to their variable, so the left by y and the right by x
y+ c_{1}= \frac{x^4}{4}cos^2y-\frac{x^2}{2}sin2y+c_{2}
let c = c2-c1 and you find
y= \frac{x^4}{4}cos^2y-\frac{x^2}{2}sin2y+c
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