15.14.22 problem 22

Internal problem ID [3194]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 23, page 106
Problem number : 22
Date solved : Monday, January 27, 2025 at 07:25:50 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime }&={\mathrm e}^{x} \left (\sin \left (x \right )-x^{2}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 43

dsolve(diff(y(x),x$3)-diff(y(x),x)=exp(x)*(sin(x)-x^2),y(x), singsol=all)
 

\[ y = -c_2 \,{\mathrm e}^{-x}+\frac {\left (-20 x^{3}+90 x^{2}-210 x +120 c_{1} -12 \cos \left (x \right )-36 \sin \left (x \right )+225\right ) {\mathrm e}^{x}}{120}+c_3 \]

✓ Solution by Mathematica

Time used: 0.755 (sec). Leaf size: 63

DSolve[D[y[x],{x,3}]-D[y[x],x]==Exp[x]*(Sin[x]-x^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{24} e^x \left (-4 x^3+18 x^2-42 x+45\right )-\frac {3}{10} e^x \sin (x)-\frac {1}{10} e^x \cos (x)+c_1 e^x-c_2 e^{-x}+c_3 \]