4.26 Problems 1251 to 1300

   4.26.1 \(y''(x)+3 y'(x)+2 y(x)=e^x+\sin (x)\)
   4.26.2 \(y''(x)-3 y'(x)+2 y(x)=x^2+2 e^{-x}\)
   4.26.3 \(y''(x)-3 y'(x)+2 y(x)=x e^{a x}\)
   4.26.4 \(y''(x)-3 y'(x)-4 y(x)=0\)
   4.26.5 \(y''(x)-3 y'(x)-4 y(x)=10 \cos (2 x)\)
   4.26.6 \(y''(x)-4 y'(x)+4 y(x)=0\)
   4.26.7 \(y''(x)-4 y'(x)+4 y(x)=e^{2 x} \cos ^2(x)\)
   4.26.8 \(y''(x)+4 y'(x)+5 y(x)=0\)
   4.26.9 \(y''(x)+4 y'(x)+5 y(x)=\sin (x)\)
   4.26.10 \(y''(x)-4 y'(x)+13 y(x)=0\)
   4.26.11 \(y''(x)-5 y'(x)+6 y(x)=0\)
   4.26.12 \(y''(x)-5 y'(x)+6 y(x)=4 e^x x^2\)
   4.26.13 \(y''(x)-5 y'(x)+6 y(x)=e^{a x}\)
   4.26.14 \(y''(x)+6 y'(x)+9 y(x)=0\)
   4.26.15 \(y''(x)+6 y'(x)+9 y(x)=e^{-3 x} \cosh (x)\)
   4.26.16 \(y''(x)-7 y'(x)+12 y(x)=0\)
   4.26.17 \(y''(x)-7 y'(x)+12 y(x)=x\)
   4.26.18 \(y''(x)+8 y'(x)+16 y(x)=0\)
   4.26.19 \(y''(x)+8 y'(x)+16 y(x)=4 e^x-e^{2 x}\)
   4.26.20 \(y''(x)-9 y'(x)+20 y(x)=0\)
   4.26.21 \(y''(x)-9 y'(x)+20 y(x)=e^{3 x} x^2\)
   4.26.22 \(2 a y'(x)+b^2 y(x)+y''(x)=0\)
   4.26.23 \(2 a y'(x)+b^2 y(x)+y''(x)=c \sin (k x)\)
   4.26.24 \(a^2 y(x)-2 a y'(x)+y''(x)=e^x\)
   4.26.25 \(\left (a^2+b^2\right )^2 y(x)-4 a b y'(x)+y''(x)=0\)
   4.26.26 \(a y'(x)+b y(x)+y''(x)=0\)
   4.26.27 \(a y'(x)+b y(x)+y''(x)=f(x)\)
   4.26.28 \(a y'(x)+y(x) (b+c x)+y''(x)=0\)
   4.26.29 \(a y'(x)+y(x) \left (b+c x^2\right )+y''(x)=0\)
   4.26.30 \(a y'(x)+y(x) \left (b+c e^x\right )+y''(x)=0\)
   4.26.31 \(b e^{2 a x} y(x)+a y'(x)+y''(x)=0\)
   4.26.32 \(a y'(x)+b e^{k x} y(x)+y''(x)=0\)
   4.26.33 \(y''(x)+x y'(x)+y(x)=0\)
   4.26.34 \(y''(x)+x y'(x)-y(x)=0\)
   4.26.35 \(y''(x)-x y'(x)+2 y(x)=0\)
   4.26.36 \(n y(x)+y''(x)-x y'(x)=0\)
   4.26.37 \(-a y(x)+y''(x)-x y'(x)=0\)
   4.26.38 \(y''(x)-x y'(x)-(1-x) y(x)=0\)
   4.26.39 \(y''(x)-2 x y'(x)+6 y(x)=0\)
   4.26.40 \(y''(x)+2 x y'(x)-8 y(x)=0\)
   4.26.41 \(2 n y(x)+y''(x)-2 x y'(x)=0\)
   4.26.42 \(-\left (-x^2-x+1\right ) y(x)+y''(x)-(2 x+1) y'(x)=0\)
   4.26.43 \(2 \left (2 x^2+1\right ) y(x)+y''(x)+4 x y'(x)=0\)
   4.26.44 \(-\left (3-4 x^2\right ) y(x)+y''(x)-4 x y'(x)=0\)
   4.26.45 \(-\left (3-4 x^2\right ) y(x)+y''(x)-4 x y'(x)=e^{x^2}\)
   4.26.46 \(a^2 x^2 y(x)-2 a x y'(x)+y''(x)=0\)
   4.26.47 \(a x y'(x)+b y(x)+y''(x)=0\)
   4.26.48 \((a+b x) y'(x)+c y(x)+y''(x)=0\)
   4.26.49 \((\text {a0}+\text {b0} x) y'(x)+y(x) (\text {a1}+\text {b1} x)+y''(x)=0\)
   4.26.50 \((\text {a0}+\text {b0} x) y'(x)+y(x) \left (\text {a1}+\text {b1} x+\text {c1} x^2\right )+y''(x)=0\)