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Solve the initial value problem.
y′′+y=1, y(0)=2, y′(0)=7.
find general solution and singular solution of xp^2+xp-yp+1-y=0
Find the exact and non-exact differential equation from the following differential equations and solve it.
(a) (𝗑2 + 𝑦2 − 1)𝑑𝗑 − 2𝗑𝑦𝑑𝑦 = 0
(b) (𝗑3 + 𝗑𝑦2 − 2𝑎2)𝑑𝗑 + (𝗑2𝑦 − 𝑦3 − 𝑦𝑏2)𝑑𝑦 = 0
Find the linear and Bernoulli’s differential equations from the following differential equations and solve it.
i) (1 − 𝗑2) 𝑑𝑦 − 𝗑𝑦 = 1.
ii) 𝑑𝑦/dx = 𝗑𝑦2 − 𝗑𝑦.
Obtain the partial differential equation of all spheres whose centres lie on z-axis with a given radius 'a'
Solve by method of variation of parameters.
d^y/dx^2 + dy/dx + 1 = e^x
For an electric circuit with L=0.05 henry, R=20 ohms and C=100*10^-6 farad, the applied emf is 100 volts. Prove that the charge q at time 't' is given by q(t) =0.01-e^(-200t) [0.01 cos(400t) +0.02 sin(400t) ] if initially q=0 and i=0.
Find the exact and non-exact differential equation from the following differential equation (x^3+x*y^2-2*a^2)dx+(x^2*y-y^3-y*b^2)dy=0
Find the order and degree of the following differential equation 2(d^2y/dx^2)-3*(dy/dx)+y=0
find the order and degree of the following differential equation (d^3*y/dx^3)^2-3*(d^2*y/dx^2)+4y=0
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#339914 on Dec 2023