60.3.33 problem 1034

Internal problem ID [11043]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1034
Date solved : Monday, January 27, 2025 at 10:42:26 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve(diff(diff(y(x),x),x)-diff(y(x),x)+exp(2*x)*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} \sin \left ({\mathrm e}^{x}\right )+c_{2} \cos \left ({\mathrm e}^{x}\right ) \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 20

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

\[ y(x)\to c_1 \cos \left (e^x\right )+c_2 \sin \left (e^x\right ) \]