76.12.8 problem 8

Internal problem ID [17564]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.2 (Theory of second order linear homogeneous equations). Problems at page 226
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 10:44:08 AM
CAS classification : [NONE]

\begin{align*} y^{\prime \prime }-\frac {t}{y}&=\frac {1}{\pi } \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=y_{0}\\ y^{\prime }\left (0\right )&=y_{1} \end{align*}

✗ Solution by Maple

dsolve([diff(y(t),t$2)-t/y(t)=1/Pi,y(0) = y__0, D(y)(0) = y__1],y(t), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 9

DSolve[{D[y[t],{t,2}]-t/y[t]==1/Pi,{y[0]==y0,Derivative[1][y][0]==y1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\pi t \]