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Homework answers / question archive / Solve the initial-value problem explicitly
Solve the initial-value problem explicitly.
dudx=7x6−3x2+7dudx=7x6−3x2+7 and u=0u=0 when x=1x=1.
u=____
First, we integrate the function:
u=∫dudxdxu=∫7x6−3x2+7dxu=x7−x3+7x+Cu=∫dudxdxu=∫7x6−3x2+7dxu=x7−x3+7x+C
Now, we use the initial value u(1)=0u(1)=0 to solve for the constant of integration:
0=u(1)0=17−13+7(1)+C0=7+CC=−70=u(1)0=17−13+7(1)+C0=7+CC=−7
Finally, we have the solution:
u=x7−x3+7x−7
