Learn Questions from a handpicked tutor in LIVE 1-to-1 classes

Find an explicit solution of the given initial-value problem. x2(dy/dx) = y - xy, y(-1) = -4
Solution:
Given: Differential equation is x2(dy/dx) = y - xy, y(-1) = -4
Rearrange the terms in terms of dy/dx
dy/dx = y(1 - x)/x2
(1/y)dy/dx = (1 - x)/x2
(1/y)dy = (1 - x)/ x2dx
Integrate on both sides, we get
∫(1/y)dy = ∫(1 - x)/x2dx
ln|y| + c = -ln|x| - 1/x
-1/x - ln|x| = ln|y| + c --- (a)
Given: When x = -1, y = -4, substitute in eq(a)
-1/-1 - ln|-1| = ln|-4| +c
1 - 0 = 1.38 + c
c = -0.38
The solution is ln|y| = -1/x - ln|x| + 0.38
Find an explicit solution of the given initial-value problem. x2(dy/dx) = y - xy, y(-1) = -4
Summary:
The explicit solution of the given initial-value problem. x2(dy/dx) = y - xy, y(-1) = -4 is ln|y| = -1/x - ln|x| + 0.38
Math worksheets and
visual curriculum
visual curriculum