Internal problem ID [2197]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 20, page 90
Problem number: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {4 y^{\prime \prime }-4 y^{\prime }+y={\mathrm e}^{\frac {x}{2}} \ln \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(4*diff(y(x),x$2)-4*diff(y(x),x)+y(x)=exp(x/2)*ln(x),y(x), singsol=all)
\[ y = c_{2} {\mathrm e}^{\frac {x}{2}}+{\mathrm e}^{\frac {x}{2}} x c_{1} +\frac {{\mathrm e}^{\frac {x}{2}} x^{2} \left (2 \ln \left (x \right )-3\right )}{16} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 38
DSolve[4*y''[x]-4*y'[x]+y[x]==Exp[x/2]*Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{16} e^{x/2} \left (-3 x^2+2 x^2 \log (x)+16 c_2 x+16 c_1\right ) \]