Internal problem ID [13683]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 21. Nonhomogeneous equations in general. Additional exercises page
391
Problem number: 21.11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y=10 x +12} \] With initial conditions \begin {align*} [y \left (1\right ) = 6, y^{\prime }\left (1\right ) = 8] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve([x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+6*y(x)=10*x+12,y(1) = 6, D(y)(1) = 8],y(x), singsol=all)
\[ y \left (x \right ) = 5 x^{3}-6 x^{2}+5 x +2 \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 20
DSolve[{x^2*y''[x]-4*x*y'[x]+6*y[x]==10*x+12,{y[1]==6,y'[1]==8}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 5 x^3-6 x^2+5 x+2 \]