Answer to Question #263031 in Differential Equations for Neilmar

Question #263031

Solve the given differential equation by using an appropriate substitution. The DE is of the form dy dx = f(Ax + By + C)




dy/dx = cos(x + y)

1
Expert's answer
2021-11-11T12:23:52-0500

u=x+yu=x+y

y=u1y'=u'-1

ucosu1=0u'-cosu-1=0


ucosu+1=1\frac{u'}{cosu+1}=1


ducosu+1=dx\frac{du}{cosu+1}=dx


ducosu+1=dx\int\frac{du}{cosu+1}=\int dx


tan(u/2)=x+ctan(u/2)=x+c


tan((x+y)/2)=x+ctan((x+y)/2)=x+c


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment