Internal problem ID [10267]
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 7.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y-\left (\ln \relax (x )+1\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(x^4*diff(y(x),x$4)+6*x^3*diff(y(x),x$3)+9*x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+y(x)=(1+ln(x))^2,y(x), singsol=all)
\[ y \relax (x ) = \ln \relax (x )^{2}+2 \ln \relax (x )-3+c_{1} \cos \left (\ln \relax (x )\right )+c_{2} \sin \left (\ln \relax (x )\right )+c_{3} \cos \left (\ln \relax (x )\right ) \ln \relax (x )+c_{4} \sin \left (\ln \relax (x )\right ) \ln \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.123 (sec). Leaf size: 39
DSolve[x^4*y''''[x]+6*x^3*y'''[x]+9*x^2*y''[x]+3*x*y'[x]+y[x]==(1+Log[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (\log (x)-1) (\log (x)+3)+(c_2 \log (x)+c_1) \cos (\log (x))+(c_4 \log (x)+c_3) \sin (\log (x)) \\ \end{align*}