
Concept explainers
Program Description: Purpose ofproblem is to calculate the general solution of the differential equation x3+3y−xy′=0 .

Explanation of Solution
Given information:
The differential equation is x3+3y−xy′=0 .
Explanation:
The given differential equation can be written as,
xdydx−3y=x3dydx−3xy=x3xdydx−3xy=x2
The above equation is a linear first order differential equation and its solution is calculated as,
ye−3∫1xdx=∫x2e−∫3xdxdxye−3lnx=∫x2e−3lnxdxyelnx−3=∫x2elnx−3dxyx−3=∫x2x−3dx
Simplify the above equation.
yx−3=∫1xdxyx−3=C+lnxy=x3(C+lnx)
Conclusion:
Thus, the solution of the differential equation x3+3y−xy′=0 is y=x3(C+lnx) .
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Chapter 1 Solutions
MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- For Differential Equations and Boundary Value Problems: Computing and Modeling Tech Update
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