Homework SourseFind the particular solution of the differential equation dy
Find the particular solution of the differential equation dy/dx=(x-4)e^(-2y) satisfying the initial condition y(4)=ln(4). The answer should be a function of \"x\".
Solution
dy/dx=(x-4)e^(-2y)
dye^(2y)=(x-4)dx
e^2y /2= (x^2 /2 -4x)+c
e^2y=x^2-8x+c
y(4)=ln(4)
e^2ln4=4^2-32+c
==>16=16-32+c
==>c=32
==>e^2y=x^2-8x+32
or y=ln(x^2-8x+32)
![Find the particular solution of the differential equation dy/dx=(x-4)e^(-2y) satisfying the initial condition y(4)=ln(4). The answer should be a function of \](/WebImages/12/find-the-particular-solution-of-the-differential-equation-dy-1010286-1761521439-0.webp "Find the particular solution of the differential equation dy/dx=(x-4)e^(-2y) satisfying the initial condition y(4)=ln(4). The answer should be a function of \")
