62.25.4 problem Ex 4

Internal problem ID [12936]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 48. Page 103
Problem number : Ex 4
Date solved : Tuesday, January 28, 2025 at 04:44:23 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=x \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 23

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

\[ y = -\frac {5}{4}+{\mathrm e}^{2 x} c_{2} +\left (x c_3 +c_{1} \right ) {\mathrm e}^{x}-\frac {x}{2} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 35

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

\[ y(x)\to c_1 e^x+x \left (-\frac {1}{2}+c_2 e^x\right )+c_3 e^{2 x}-\frac {5}{4} \]