62.29.10 problem Ex 12

Internal problem ID [12961]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 52. Summary. Page 117
Problem number : Ex 12
Date solved : Tuesday, January 28, 2025 at 04:45:28 AM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+5 y^{\prime }-2 y&={\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 32

dsolve(diff(y(x),x$4)-diff(y(x),x$3)-3*diff(y(x),x$2)+5*diff(y(x),x)-2*y(x)=exp(3*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-2 x} \left (\left (c_4 \,x^{2}+x c_3 +c_{1} \right ) {\mathrm e}^{3 x}+c_{2} +\frac {{\mathrm e}^{5 x}}{40}\right ) \]

✓ Solution by Mathematica

Time used: 0.080 (sec). Leaf size: 118

DSolve[D[y[x],{x,4}]-D[y[x],{x,3}]-3*D[y[x],{x,2}]+5*D[y[x],x]-2*y[x]==Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x x \int _1^x-\frac {1}{9} e^{2 K[2]} (3 K[2]+1)dK[2]+e^x \int _1^x\frac {1}{54} e^{2 K[1]} \left (9 K[1]^2+6 K[1]+2\right )dK[1]+\frac {1}{12} e^{3 x} x^2+c_4 e^x x^2-\frac {e^{3 x}}{135}+c_3 e^x x+c_1 e^{-2 x}+c_2 e^x \]