Internal problem ID [1137]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.6 Reduction or order. Page
253
Problem number: 31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y=4 x^{4}} \] Given that one solution of the ode is \begin {align*} y_1 &= x^{2} \end {align*}
With initial conditions \begin {align*} [y \left (-1\right ) = 7, y^{\prime }\left (-1\right ) = -8] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve([x^2*diff(diff(y(x),x),x)-3*x*diff(y(x),x)+4*y(x) = 4*x^4, x^2, y(-1) = 7, D(y)(-1) = -8],y(x), singsol=all)
\[ y \left (x \right ) = x^{2} \left (8 i \pi +x^{2}-8 \ln \left (x \right )+6\right ) \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 37
DSolve[x^2*y''[x]-3*x*y'[x]+4*y[x]==4*x^2,{y[-1]==7,y'[-1]==8},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2 \left (2 \log ^2(x)+(-22-4 i \pi ) \log (x)-2 \pi ^2+22 i \pi +7\right ) \]