78.11.16 problem 11

Internal problem ID [18287]
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 16. The Use of a Known Solution to find Another. Problems at page 121
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 08:28:37 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} y^{\prime \prime }-f \left (x \right ) y^{\prime }+\left (f \left (x \right )-1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 22

dsolve(diff(y(x),x$2)-f(x)*diff(y(x),x)+(f(x)-1)*y(x)=0,y(x), singsol=all)
 

\[ y = \left (\left (\int {\mathrm e}^{-2 x +\int f \left (x \right )d x}d x \right ) c_{1} +c_{2} \right ) {\mathrm e}^{x} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[D[y[x],{x,2}] -f[x]*D[y[x],x]+(f[x]-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved