Ans:(a)
8. specify which letter answer 2 can be &re differential equation y-- solved using the substitution...
6. specify which letter answer Y2 = it has gereral solution? ssole differential equation y = et ? by separation of variables a) y = + Y + c 4X c) y=4e y 3+C 4 4x4 b) y = - - - © y = 46 (2x) +C e + C ddy- celky ux
Identify the type of the following differential equation. Note: y is the dependant variable in the equation. dy dx -2y 2 (4+lny-lnx) Select all that apply. Seperable Linear Exact Homogeneous Bernoulli Linear Substituion Identify the type of the following differential equation. Note: y is the dependant variable in the equation. 31/2 dy - 4 = y3/2 dx Select all that apply Seperable Linear Exact Homogeneous Bernoulli Linear Substituion dy The differential equation 6 - dx 949,6 – 24 can be...
9. specify which letter answer a two lirearly independent solutions of the differential equation y"-1441-494-0 ore af y, =ė? .Yz-Xerx UX b) y, = e 1 Y2 = xex YZ = Xe²7 6 yi=ex d) es vize" Yo = ex Y2 = ex 77 1 Y = e-7x
2. Using substitution to simplify a problem (a) Solve the following (homogeneous) differential equation using the appropriate substitution. (b) Find the solution to the equation T+3 Hint: The same substitution wil no longer work, but the equation is almost homogeneous. Use a substitution of the form r- X - h, y-Y - k to reduce this problem to the problem solved in part (a), i.e. choose h and k so that this problem becomes homogeneous in the substituted variables X...
4. specify which letter answer 4) An integrating factor for the lirear differential equation Xy't xy=1 is aj o c) e) et dJ x
differential equations Consider the following differential equation to be solved using a power series. y" + xy = 0 On Using the substitution y = cryn, find an expression for Ck + 2 in terms of Ck - 1 for k = 1, 2, 3... n = 0 Ck +2= + 6 Find two power series solutions of the given differential equation about the ordinary point x = 0. x3 O Y1 = 1 - xo and y2 = x...
Consider the following differential equation to be solved using a power series. y" - y' = 0 Using the substitution y = į coxn, find an expression for Ck + 2 in terms of Ck + 1 for k = 0, 1, 2, .... k+2= + + + Find two power series solutions of the given differential equation about the ordinary point x = 0. Compare the s 4.3. Try to explain any differences between the two forms of the...
12. specify which letter answer is correct dj yp=é 2 Otwo linearly independene solotions of the I differential equation ý "+12ylt 36y=o are 064 Y₂ = Xe6x b) y,=0 Y = xe Y = 6x d Yizes Y = 0 6x Y = xe 6x Vi=e6x Y2= e 6x
11. please show all work and specify which letter answer If one solution of the differential Y"+2ylty=0 is yi=e* Use method of reduction order (lety-oy), a second linearly independent solution is a) y = et c) y=xe* e) y e* 6) y=xe d) y=c
An equation in the form with is called a Bernoulli equation and it can be solved using the substitution which transforms the Bernoulli equation into the following first order linear equation for : Given the Bernoulli equation we have so . We obtain the equation . Solving the resulting first order linear equation for we obtain the general solution (with arbitrary constant ) given by Then transforming back into the variables and and using the initial condition to find ....