Question 1 (PLO-2,CLO-2,C3)Marks-(12+13 a) Solve the following Differential Equation. (x2 – 3y2)dx + 2xydy = 0 b) Demonstrate whether the given differential equation is exact.If it is exact, Solve it. x+y dx dy = 0 y-1 2 y-1
a.) Solve the following IVP. X !=3x,-13x2 X, (O)=3 X2 = 5x +X2 X₂(0)=-10 b.) solve the following IVP. X;= -X, +(3/2) X2 X, (2)=1 X 2 = (-%6) xx-2x2 X2 (2)=0
1. Use Cramer's rule to solve the following equation systems: (a) 3x1 - 2x2 = 6 (C) 8x1 - 7x2 = 9 2x1 + x2 = 11 X1 + X2 = 3 (b) -- X1 + 3x2 = -3 (d) 5x1 + 9x2 = 14 4x1 - x2 = 12 7x1 - 3x2 = 4
SOLVE FOR X y = -x2 + 1 2 points Solve the quadratic equation by factoring (a calculator solution is not acceptable): 3x2 + 5x – 2 = 0 Separate multiple answers with a comma, and type fractions using the /' key if necessary. type your answer...
6. Solve the differential equation by variation of parameters. y" – 2y' + y = 1+x2
6. Solve the system of first order differential equations: x'(t) = X1 + X2 x2(t)x 3x2 6. Solve the system of first order differential equations: x'(t) = X1 + X2 x2(t)x 3x2
4. Solve the following equation using integration by parts. (10 Marks) | 22 x2 In(x) dx 5. Calculate the shaded area between the curve and the x-axis as shown below. (5 Marks) y = x2 - 6x
3. Use Cramer's rule to solve the following equation systems: (a) 8x1 - x2 = 16 (©) 4x + 3y - 2z=1 2x2 + 5x3 = 5 x + 2y = 6 2X1 + 3x3 = 7 3x + Z=4 (6) - X1 + 3x2 + 2x3 = 24 (d) -x + y +7= a X, + x3 = 6 x-y+z=b Sx2 - X+Y-7=C X3 = 8
solve the differential equation dy y(x - y) dx x2
B.6-2 Using a matrix approach, solve the following system of equations: X1+z+x=4 X1 + X2 +43-44 =2 X=n=0 12-1===