Class 12 Maths Differential Equations General and Particular Solution of Differential Equation

General and Particular Solution of Differential Equation But for differential equation like y’-sinx=0. Solution of y is in function in terms of variables not in numbers. We classify solution of differential equation into two parts-

1. General Solution
2. Particular Solution

Let us understand General solution of differential equation with an example.
Example:
dy/dx - k sin(x) = 0  – A differential equation

Integrating both side
∫dy =  ∫dx * k sin(x)

We get solution as  y=-Kcosx+c

This is called a “general solution” of a differential equation as we get the solutions in constant form of K and C (k and c can be any value from - ∞ to + ∞ )

Particular solution:
Now the solution we get is a General solution but if we assign some value to it by giving some conditions Let’s say we get the value of k and c be -4 and 7 resp. then the equation will became

y=4cosx+7      -  This equation is a particular solution of a given differential equation.

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