Homework Statement
Find the particular solution of the differential equation
\frac{dy}{dx}+ycos(x)=3cos(x)
Homework Equations
y(0)=5
The Attempt at a Solution
\frac{dy}{dx}=3cos(x)-ycos(x)
\frac{dy}{dx}=(cos(x))(3-y)
\int \frac{dy}{3-y}=\int cos(x) dx
-ln|3-y|=sin(x)+C...
Homework Statement
The differential equation dy/dx= 35/(y1/8+25x2y1/8 has an implicit general solution of the form F(x,y)=K. In fact, because the differential equation is separable, we can define the solution curve implicitly by the form F(x)=G(x)+H(y)=K.
Find such solution and then give the...
Homework Statement
dx/dy=-0.6y
y(0)=5
Homework Equations
The Attempt at a Solution
I tried solving it by
\intdy/y=\int-0.6dx
ln(y)=-0.6x+c
ln(y(0))=-0.6(0)+c
ln(5)=c
ln(y)=-0.6x+ln(5)
y=e^{-0.6x}+5
But its incorrect. I don't know what I am doing wrong. Can someone helping...