60.3.62 problem 1063

Internal problem ID [11072]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1063
Date solved : Monday, January 27, 2025 at 10:43:45 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-\left (2 \,{\mathrm e}^{x}+1\right ) y^{\prime }+{\mathrm e}^{2 x} y-{\mathrm e}^{3 x}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.706 (sec). Leaf size: 34

dsolve(diff(diff(y(x),x),x)-(2*exp(x)+1)*diff(y(x),x)+exp(2*x)*y(x)-exp(3*x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{\frac {x}{2}+{\mathrm e}^{x}} \sinh \left (\frac {x}{2}\right ) c_{2} +{\mathrm e}^{\frac {x}{2}+{\mathrm e}^{x}} \cosh \left (\frac {x}{2}\right ) c_{1} +2+{\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.075 (sec). Leaf size: 66

DSolve[-E^(3*x) + E^(2*x)*y[x] - (1 + 2*E^x)*D[y[x],x] + D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{e^x} \left (\int _1^x-e^{3 K[1]-e^{K[1]}}dK[1]+e^x \int _1^xe^{2 K[2]-e^{K[2]}}dK[2]+c_2 e^x+c_1\right ) \]