Solution Found!
In 23 and 24 the indicated functions are known linearly
Chapter 4, Problem 23E(choose chapter or problem)
In Problems 23 and 24 the indicated functions are known linearly independent solutions of the associated homogeneous differential equation on (0, ). Find the general solution of the given nonhomogeneous equation.
\(x^{2} y^{\prime \prime}+x y^{\prime}+\left(x^{2}-\frac{1}{4}\right) y=x^{3 / 2} \)
\(y_{1}=x^{-1 / 2} \cos x, y_{2}=x^{-1 / 2} \sin x\)
Text Transcription:
x^{2} y^{\prime \prime}+x y^{\prime}+\left(x^{2}-\frac{1}{4}\right) y=x^{3 / 2}
y_{1}=x^{-1 / 2} \cos x, y_{2}=x^{-1 / 2} \sin x
Questions & Answers
QUESTION:
In Problems 23 and 24 the indicated functions are known linearly independent solutions of the associated homogeneous differential equation on (0, ). Find the general solution of the given nonhomogeneous equation.
\(x^{2} y^{\prime \prime}+x y^{\prime}+\left(x^{2}-\frac{1}{4}\right) y=x^{3 / 2} \)
\(y_{1}=x^{-1 / 2} \cos x, y_{2}=x^{-1 / 2} \sin x\)
Text Transcription:
x^{2} y^{\prime \prime}+x y^{\prime}+\left(x^{2}-\frac{1}{4}\right) y=x^{3 / 2}
y_{1}=x^{-1 / 2} \cos x, y_{2}=x^{-1 / 2} \sin x
ANSWER:Step 1 of 5
Given that
We have to find the general solution of the nonhomogeneous equation.