Solve 2y"'+y'-4y= cosh5x y(0)=en y'(0)=- e
solve the following differential equations
1. (1 + 2 𝑒 𝑥 𝑦) + 2𝑒 𝑥 𝑦 (1 − 𝑥 𝑦 ) 𝑑𝑦 𝑑𝑥 = 0
2.1. 𝑡𝑎𝑛 𝑥 . 𝑠𝑖𝑛2 𝑦 𝑑𝑥 + 𝑐𝑜𝑠2 𝑥 . 𝑐𝑜𝑡 𝑦 𝑑𝑦 = 0
2. (1 + 2 𝑒 𝑥 𝑦) + 2𝑒 𝑥 𝑦 (1 − 𝑥 𝑦 ) 𝑑𝑦 𝑑𝑥 = 0
3. (𝑥 − 2𝑦 + 1) 𝑑𝑥 + (4𝑥 − 3𝑦 − 6) 𝑑𝑦 = 0
4. 𝑦(𝑥 3 𝑒 𝑥𝑦 − 𝑦) 𝑑𝑥 + 𝑥 (𝑦 + 𝑥 3𝑒 𝑥𝑦) 𝑑𝑦 = 0
5. 𝑦 2 𝑑𝑥 + (𝑥 2 − 𝑥𝑦 − 𝑦 2 ) 𝑑𝑦 = 0
6. (4𝑒 −𝑦 𝑠𝑖𝑛 𝑥 − 1) 𝑑𝑥 − 𝑑𝑦 = 0
7. 𝑥 4 𝑑𝑦 𝑑𝑥 + 𝑥 3𝑦 − 𝑠𝑒𝑐(𝑥𝑦) = 0
8. (1 + 𝑠𝑖𝑛 𝑦) 𝑑𝑥 𝑑𝑦 = 2𝑦 𝑐𝑜𝑠 𝑦 − 𝑥(𝑠𝑒𝑐 𝑦 + 𝑡𝑎𝑛 𝑦)
The amount A in a fixed account at any time t is known to satisfy the the differential equation
d2A/dt2+tdA/dt+(t2-4)A=0. Express A as a series in powers of t.
Using Taylor series expression, find a power series solution for the equation
2x2d2y/dx2-xdy/dx+(x-5)y=0 in powers of (x-1) if y(1)=4 and y'(1)=2
lx=100000-50x2
lx=100000+50(1+x)2 For the chosen models determine the radix
The population P, t years after the initial observation is given by the formula:
pt=(100000)/(2+3e-0.05t)
Determine the exact size of the population and the time in years when the rate of growth is maximum
Find the relation of the variable w if the growth rate is given by
dw/dt=(kw(α-w))/α, k>0, at t=0,w=α/(1+β)
Using annihilator method obtain particular solution of y"'+y= cosx+sinx