Differential Equations Answers

x^2d^2y/dx^2-xdy/dx+y=log x+sin(log x)+1/x

In the following problem use a suitable substitution to reduce the order of the given DE and then solve it

1. y''=2y'
2. y''+e^yy'2=0
3. y"+(1-1/y)y'²=0

The rate constant for the radioactive disintegration of ⁶⁰₂₇Co is 0.1317 year".

Calculate the mass of .₂₇⁶⁰Co that will remain after 21.04 years out of 1 gram sample.

Solve x2p+y2q=(x+y)z

(x + 2) - (d ^ 2 * y)/(d * x ^ 2) - (2x + 5) * (dy)/(dx) + 2y; =(x+1) ex

xy"+2y'=0 reduced into y

Solution of the equation of the form (d ^ 2 * y)/(d * x ^ 2) + P * (dy)/(dx) + Qy = 0 is known as (a) Auxiliary equation (b) Complementary function (c) Particular integral (d) Singular solution (e) None of these

singular and general solution 

e^3x(p-1)+p^3e^2y=0;X=e^x ,Y=e^y by substitution

find general and singular solution y=2xp+4yp^2;X=x,Y=y^2 ,by using clairat's equation

Solve the following equations by the use of the operator D

1. D²y -2Dy + y= sinx +x²

2.D²y -6Dy +6y= e^3x + e^-3x