Internal problem ID [6286]
Book: Selected problems from homeworks from different courses
Section: Math 2520, summer 2021. Differential Equations and Linear Algebra. Normandale college,
Bloomington, Minnesota
Problem number: HW 5 problem 1(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-4 y^{\prime }+3 y-9 x^{2}-4=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 6, y^{\prime }\relax (0) = 8] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve([diff(y(x),x$2)-4*diff(y(x),x)+3*y(x)=9*x^2+4,y(0) = 6, D(y)(0) = 8],y(x), singsol=all)
\[ y \relax (x ) = 2 \,{\mathrm e}^{3 x}-6 \,{\mathrm e}^{x}+3 x^{2}+8 x +10 \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 26
DSolve[{y''[x]-4*y'[x]+3*y[x]==9*x^2+4,{y[0]==6,y'[0]==8}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x (3 x+8)-6 e^x+2 e^{3 x}+10 \\ \end{align*}