Internal problem ID [1111]
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: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=7 \,{\mathrm e}^{x} x^{\frac {3}{2}}} \] Given that one solution of the ode is \begin {align*} y_1 &= {\mathrm e}^{x} \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve([diff(y(x),x$2)-2*diff(y(x),x)+y(x)=7*x^(3/2)*exp(x),exp(x)],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} c_{2} +x \,{\mathrm e}^{x} c_{1} +\frac {4 x^{\frac {7}{2}} {\mathrm e}^{x}}{5} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 29
DSolve[y''[x]-2*y'[x]+y[x]==7*x^(3/2)*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{5} e^x \left (4 x^{7/2}+5 c_2 x+5 c_1\right ) \]