# Formation of a Differential Equation whose General Solution is given

• The order of a differential equation representing a family of curves is same as the number of arbitrary constants present in the equation corresponding the family of curves.
• To form a differential equation from a given function we differentiate the function successively as many times as the number of arbitrary constants in the given function and then eliminate the arbitrary constants.

### Part3: View the Topic in this video From 00:12 To 07:02

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• The differential equation of y = Aeαx + Beβx is \frac{d^{2}y}{dx^{2}}-(\alpha+\beta)\frac{dy}{dx}+\alpha\beta y = 0
• The differential equation of y = (A + Bx) ekx is \frac{d^{2}y}{dx^{2}}-2k\frac{dy}{dx}+k^{2} y = 0
• The differential equation of y = A cos kx + B sin kx by eliminating A and B is \frac{d^{2}y}{dx^{2}}+k^{2} y = 0
• The differential equation of y = Aekx + Be-kx by eliminating A and B is \frac{d^{2}y}{dx^{2}}-k^{2} y = 0
• The differential equation of y = ex (A cos nx + B sin nx) by eliminating A and B is y2 − 2y1 + (n2 + 1) y = 0
• The differential equation of y = ekx (A + Bx + Cx2) by eliminating A, B, C is y3 − 3ky2 + 3k2 y1 − k3 y = 0
• The differential equation of y = ekx (A cos (lx)) + (B sin (lx)) by eliminating A, B is y2 − 2ky1 + (k2 + l2) y = 0