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Differential Equations
- Consider the system of linear equations in x and y. ax+by=ecx+dy=f Under what conditions will the system have exactly one solution?arrow_forwardFind a system of two equations in two variables, x1 and x2, that has the solution set given by the parametric representation x1=t and x2=3t4, where t is any real number. Then show that the solutions to the system can also be written as x1=43+t3 and x2=t.arrow_forwardFind a system of two equations in three variables, x1, x2 and x3 that has the solution set given by the parametric representation x1=t, x2=s and x3=3+st, where s and t are any real numbers. Then show that the solutions to the system can also be written as x1=3+st,x2=s and x3=t.arrow_forward
- Use a system of linear equation to find the parabola y=ax2+bx+c that passes through the points (1,2), (0,1) and (2,6)arrow_forwardPlease hand write or somehow make the work clear. I can't read it when its all jumbled together with typing.arrow_forwardFind two linearly independent solutions of 2x2y"-xy'+(-6x+1)y=0, x>0 of the formarrow_forward
- Y₁ = 1+ a3x³ + A6㺠+... Y₂ = x + b₁x¹ +b7x7 +... Enter the first few coefficients: Az = a6 = b₁ b7 ) Find two linearly independent solutions of y" + 6xy = = - 0 of the formarrow_forwardShow solutionarrow_forwardUse the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. x' = 9x - 10y + sint and y' = 5x - y - cost. Write the system in operator form.arrow_forward
- Show that the homogenous equation(Ax + By) ⅆx + (Cx + Dy) ⅆy = 0Is exact if and only if B = C. Show that the homogenous equation(Ax2 + Bxy + Cy2) ⅆx + (Dx2 + Exy + Fy2) ⅆy = 0Is exact if and only if B = 2D and E = 2C.arrow_forwardUse the finite difference method to solve the system of equation given by: y"+ 2y" + y' +y = x² y(0) = 0.2, y(1) = 0.8, & y(2) = 0.2arrow_forwardCalculate (x+y+z) ds where C is the intersection of x +y +2 =2 and z=-arrow_forward
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