|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-
Let us understand General solution of differential equation with an 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 + ∞ )
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.