Thursday, December 22, 2011

Solve the Differential Equation: y'=(3x^2)/(y^3) where y(1)=2

Solve the differential equation y'=3x^2/y^3 where y(1)=2:





Rewrite with dy/dx:

Multiply both sides by y^3

Multiply both sides by dx. We now have our variables separated and ready to integrate:

Integrating both sides:

Using y(1)=2 to solve for C, we find that C = 3.


Our new equation with C:

Multiplying both side by 4:

Taking the 4th root of both sides to solve for y gives us our final answer:


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