let y!l-3y'+2y=e ,y(0) =1 ,y' (0) =0 , find L (y) s2 - 4s+6 .a O (s-3) (s-2) (s- 1) s2 - 5s+12 .b O (s-3) (s-2) (s- 1) s2 – 6s+10 .c O (s-3) (s-2) (s- 1) s2- 2s+6 (s-3) (s-2) (s-1)

Q: Find y(0.2) for y"=xz²-y², xo=0,yo-1,20-0, with step length 0.2 using Runge-Kutta 2 method (2nd…

A: To find- Find y0.2 for y'' = xz2 - y2, x0 = 0, y0 = 1, z0 = 0, with step length 0.2 using…

Q: 4. For y' = y3 +y² – 6y, Find the critical points. Draw a phase diagram and mark the critical points…

A: Given y'=y3+y2-6y Given a differential equation y'=fy a point y0 is said to be a critical point if…

Q: Solution: y1 = 2.513274123; y2 = 1.814517822; y3 = 1.216364496

A: Here, initial condition is given at x = 1.Therefore, start with x0 = 1.Given equation is:

Q: 5. Find the first partial derivatives of w= In(x+2y+3z) %3D

A: The given function is w=lnx+2y+3z

Q: A researcher wants to analyze the effect of a variable x on another variable y using observations…

A: Given the estimated model for the variables x and y as I yi=β1+β2xi+ei II yi=β1+γ1ri+β2xi+γ1xi…

Q: 5) Starting from the expression Cp- Cy = T use the appropriate relations between partial derivatives…

A: The amount of heat required to raise the temperature by one degree in one mole of the substance is…

Q: Suppose z = f(x,y) is a differentiable function of two variables. What do the partial derivatives,…

A:

Q: dY 1. The system in Section 3.2 - Exercise 1 (previous page): dt Y dt -5 2. The system in Section…

A:

Q: 2. Find the four second partial derivatives x² +y2

A:

Q: Find both first partial derivatives. z = 13xy az az ду II

A:

Q: yUx-xUy=U , U(x,1)=2+e^-x

A: Given partial differential equation is, yux-xuy=u      .....1. With initial condition ux,1=2+e-x.…

Q: Find all the second partial derivatives. T = e-4r cos(0) -4r 16e cos (0) Trr %3D Tre 4e 4"sin (0)…

A:

Q: 8 Find all the first partial derivatives of z = 5x°y - 8x y. (Choose all applicable answers.) O zy =…

A:

Q: Considor tho initial valuo problom (z - 9)y" + 4y = a with initial conditions y(0) = 4 and y (0) =…

A: Consider an IVP y''+p(x)y'+q(x)y=f(x). The initial conditions are y(x0)=y0 and y'(x0)=y0'. Then if…

Q: 4. At high temperatures, nitrogen dioxide, NO2, decomposes into NO and O2. If y(t) is the…

A: Given: y(t) changes according to the law, dydt=-0.05y2 where, y is the concentration in moles per…

Q: integrate dy/(sb - smy-bny-nmy^2

A: SOLUTION-

Q: 3 (D2 + 4)y =- Ost<3 3t +2 t23 y(0)=0, y'(0)=1 Find L{y} °L{y} = 1 3. 3e 3s Se-3s 82+4 s(s2+4) s (s²…

A:

Q: 2. z = ²+² У Х

A:

Q: Find the first partial derivatives of 3x - y f(x, y) = 3x + Y at the point (x, y) = (4, 4). af (4,…

A:

Q: Solution: y1 = 1.200000000; y2 =2.085625000; y3 = 3.079099746

A: Here, initial condition is given at x = 2.Therefore, start with x0 = 2.Given equation is:

Q: 1 Find the partial derivative with respect to y of the function (2 x – 3) (3 y + 1)i el-5 z+5). -5…

A: To find the partial derivative of the given function with respect to y (2x-3)1/4(3y+1)1/4e(-5z+5)

Q: (2t - 4 0st<2 (D2 – 1)y =- 12 %3D t22 y(0)=0, y'(O)=1 Find L{y} L (y) = F1) 4 2e-2s 2e-2s %3D -…

A:

Q: Solution: y1 = 1.450000000; y2= 2:085625000; y3 = 3:079099746

A: Here, initial condition is given at x = 2.Therefore, start with x0 = 2.Given equation is:

Q: Find the first partial derivatives of f(x, y) - 4 - (x - 4)?- (y + 3)? by holding first y, then x,…

A: Partial differentiation of function f(x,y) means differentiating with respect to one variable…

Q: Find both first partial derivatives. z = 4y²/x az ax az ду || ||

A: z=4y2x

Q: Find the solution of the differential formula in partial derivatives = x³ sent +1; y(x,t);…

A: Integrate twice with respect to t and then put conditions

Q: Suppose there are two tanks, each containing 20 L of fluid. Tank 1 initially contains water with 4kg…

A: The given system is as follows: Here, pure water is pumped in to each of the tanks. Suppose after…

Q: Test 1. y" - y - 2y = e by D- operator method 2. y" - 3y' +2y = ex + 6x3 - 2+ 3sin(4x)

A: 1. Now we will solve the differential equation. The genaral solution: =…

Q: Find the four second partial derivatives. z = y3 − 5x2y2 − 3

A: we have to find the four second partial derivatives.

Q: Reverse the order of integration 3 Lütfen birini seçin: a. 1 √3 √316 b. 1 So C. e d. 2 e. √3x 2² v²…

A:

Q: 2 Discuss the stability of equilibrium points of the following ODE: { (2 = -r³ + y°, y = -x.

A:

Q: Q.3 Determine all second order partial derívatives of (5) w = In(x² + y²)+ 2arctan| Mention any…

A: Given that  w=ln(x^2+y^2)+2arctan(y/x) To find the secondary order partial derivatives

Q: 4. (a) Prove that M(x, y) + N(x, y) = 0 can be made exact using an integrating factor that = f(x+y)…

A: To find-  Prove that Mx, y + Nx, ydydx = 0 can be made exact using an integrating factor that…

Q: Find both first partial derivatives. z = In əz əx az ? ду II

A:

Q: How many second partial derivatives does ƒ (x, y, z, t) have?

A: We have to find the number of second partial derivatives.

Q: Find all the first partial derivatives of z = 5x°y - 8xy*. (Choose all applicable answers.) O zz =…

A:

Q: 2t-4 0st<2 (D2 - 1)y = t22 y(0)=0, y'(0)=1 Find L{y} L (1) = 1 + - - 2+ 4 2e 2s 2e-2s %3D | L (y) =…

A:

Q: 5.3.21 5x cos (xy). Find the first partial derivatives for f(x,y) ox Enter your answer in the answer…

A: Given the function f(x,y)=5x cos(xy), The product rule will work the same way here as it does with…

Q: 4. A tank initially holds 80 gal of a brine solution containing 1/8 Ib of salt per gallon. At t = 0,…

A:

Q: y" + 3y' = 0, y(0) = -2, y'(0) = 3

A: The solution is given as

Q: 2t – 4 0st<2 (D² – 1)y = [2 t 2 y(0)=0, y'(O)=1 Find L{y} O L 1) = + -1) 2e-2s +. s(s² -1) 4 2e s2…

A: To solve given question first we take Laplace transform of both sides and solve.

Q: (a) Find the general solution of the equation (x – 2) y dr 3(х — 1) -y3 1 - (x + 1) (b) Given the…

A: A first-order linear ordinary differential equation(ODE) is of the form y'(x)+p(x)y=q(x). The…

Q: 1. y" - y' - 2y = e by D- | operator method 2. y" - 3y' +2y = e4x + 6x³ – 2+ 3sin(4x)

A:

Q: Consider the Initial Value Problem (IVT) dy = Axy, y(0) = 1, da where A is a positive constant. The…

A: As per the rules we can solve only 3 subparts. Please check the below answers

Q: 1. E(Y,X, X2... X) (Y+Y2 +. + Yn) 2. E(IX,, X2, X) =E Y2+ + Yp) + -B(X, +X +

A: We have to show that β¯ is conditionally distributed.  To show β¯ conditionally distributed we will…

Q: 5,2 4. Find all first and the second partial derivatives. f(x,y)=2x°y +x y

A: First order partial derivatives :fx=∂f∂x  fy=∂f∂ySecond order partial derivatives:fxx=∂2f∂x2=∂∂x∂∂x…

Q: 1 the value of ax/az at the point (1, xz + y Inx - x2 + 4 = 0 nes x as a function of the two…

A: Here the given that,  xz+yln(x)-x2+4=0 where x as a function of two independent variables y and z

Q: 2. Gauss-Seidel's Method. Stop at 4th iteration. (correct to 3 decimal places) 15x + 3y - 2z = 85…

A: Use the procedure of Gauss Seidal method with initial guess (0,0,0) to proceed further as in next…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.