Internal problem ID [11281]
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]]
\[ \boxed {x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y=\left (\ln \left (x \right )+1\right )^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
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)
\[ y \left (x \right ) = \left (c_{3} \ln \left (x \right )+c_{1} \right ) \cos \left (\ln \left (x \right )\right )+\left (c_{4} \ln \left (x \right )+c_{2} \right ) \sin \left (\ln \left (x \right )\right )+\ln \left (x \right )^{2}+2 \ln \left (x \right )-3 \]
✓ Solution by Mathematica
Time used: 0.27 (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]
\[ y(x)\to \log ^2(x)+2 \log (x)+(c_2 \log (x)+c_1) \cos (\log (x))+(c_4 \log (x)+c_3) \sin (\log (x))-3 \]