78.10.5 problem 5

Internal problem ID [18266]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 15. The General Solution of the Homogeneous Equation. Problems at page 117
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 11:44:49 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-2 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=8 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 15

dsolve([x^2*diff(y(x),x$2)-2*y(x)=0,y(1) = 1, D(y)(1) = 8],y(x), singsol=all)
 

\[ y = 3 x^{2}-\frac {2}{x} \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 16

DSolve[{x^2*D[y[x],{x,2}] -2*y[x]==0,{y[1]==1,Derivative[1][y][1]==8}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {3 x^3-2}{x} \]