Internal problem ID [7039]
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]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+3 y=9 x^{2}+4} \] With initial conditions \begin {align*} [y \left (0\right ) = 6, y^{\prime }\left (0\right ) = 8] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = -6 \,{\mathrm e}^{x}+2 \,{\mathrm e}^{3 x}+3 x^{2}+8 x +10 \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 27
DSolve[{y''[x]-4*y'[x]+3*y[x]==9*x^2+4,{y[0]==6,y'[0]==8}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 x^2+8 x-6 e^x+2 e^{3 x}+10 \]