73.16.22 problem 24.4 (d)

Internal problem ID [15534]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 24. Variation of parameters. Additional exercises page 444
Problem number : 24.4 (d)
Date solved : Tuesday, January 28, 2025 at 08:01:25 AM
CAS classification : [[_high_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 x y^{\prime }+9 y&=12 x \sin \left (x^{2}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 69

dsolve(x^4*diff(y(x),x$4)+6*x^3*diff(y(x),x$3)-3*x^2*diff(y(x),x$2)-9*x*diff(y(x),x)+9*y(x)=12*x*sin(x^2),y(x), singsol=all)
 

\[ y = \frac {\left (-2 x^{4}-2\right ) \sin \left (x^{2}\right )+16 x^{6} c_4 +2 \,\operatorname {Ci}\left (x^{2}\right ) x^{6}+16 c_{2} x^{4}-6 \,\operatorname {Si}\left (x^{2}\right ) x^{4}+c_{1} x^{2}-4 x^{2} \cos \left (x^{2}\right )+16 c_{3}}{16 x^{3}} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 101

DSolve[x^4*D[y[x],{x,4}]+6*x^3*D[y[x],{x,3}]-3*x^2*D[y[x],{x,2}]-9*x*D[y[x],x]+9*y[x]==12*x*Sin[x^2],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {8 x^2 \int _1^x\frac {3}{4} K[1] \sin \left (K[1]^2\right )dK[1]+x^6 \operatorname {CosIntegral}\left (x^2\right )-3 x^4 \text {Si}\left (x^2\right )+8 c_4 x^6+8 c_3 x^4-\sin \left (x^2\right )+x^2 \cos \left (x^2\right )+8 c_2 x^2-x^4 \sin \left (x^2\right )+8 c_1}{8 x^3} \]