Answer to Question #148603 in Differential Equations for Noku

Question

Obtain the least-order differential equation x = c1sin (y + c2)?

Answer 1

$x=c_1\sin(y+c_2)\\ \text{differentiate both sides with respect to y}\\ x'=c_1\cos(y+c_2)\\ \text{differentiate both sides with respect to y again}\\ x''=-c_1\sin(y+c_2)\\ x''=-x\\ x''+x=0.$