Question

Find the differential equation whose general solution is given by y = ₁² +₂e² + x²

Answer 1

Answer:

equation is y=(c1+c2)cos(x+c3)−c4ex+c5.

Rewriting the equation in terms of essential arbitrary constants:

y=(K1)cos(x+K2)−K3ex.

where K1=c1+c2;K2=c3;K3=c4ec5.

Hence the essential arbitrary constants are 3.

∴ The order of the differential equation is 3.

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