The differential equation whose solution is y=c₁ cosax +c₂ sinax ( . Where c₁ and c₂ are arbitrary constants) is

Step-by-step solution

Given y=c₁ a x+c₂ a x d y d x =-a c₁ a x+a c₂ a x aligned y ( 1 1-x² ) &= x (1-x² )^ 1 2 1 (1-x² ) d x &= -1 2 -2 x (1-x² )^ 3 / 2 d x= (- 1 2 ) (1-x² )^ 1 2 (- 1 2 ) +c y ( 1 1-x² ) &= 1 1-x² +c y= 1-x² +c (1-x² ) aligned