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Differential Equations and Linear Algebra (4th Edition)
- 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_forwardSolve for the particular solution of the non-homogeneous DE. y'' = 4 a. x b. 2x2 c. 1/2 x2 d. x3 / 3arrow_forwardObtain the particular solution of x²y" + xy' = 1; y = 0 and y' = 1/2, when x = 1arrow_forward
- #4 Find the general solutions of the system. x′= 2 0 −4 −1 4 −1 1 0 6 x x(t)=enter your response herearrow_forwardfind the solution satisfying the initial conditions: y''-y=x^2 , y(0)=0 , y'(0)=-1arrow_forwardWhat is the solution for the equation 2ydx+(3y-2x)dy=0 & say if what method of solution such as if it is separable, linear, exact, or etc was usedarrow_forward
- Can you solve the system of equations dx/dy = [ 15 - 18 ] [ 12 -15 ] when it has the inital value (below)? x(0) = [ 11 ] [ 8 ]arrow_forwardDo you think that the initial-value problem y'=xy^(1/2), y(0)=0 has a unique solution? Justify your answer.arrow_forwardSolve the following systems of equation: 2x + 3y = z − 13x = 8z − 15y + 7z = − 1arrow_forward
- solve the following system of equations: x'=dx/dt=7y+7e4t y'=dy/dt=5y-3e-5t x(0)=2 and y(0)=3arrow_forwardThe following problem deals with the open three-tank system. Fresh water flows into tank 1; mixed brine flows from tank 1 into tank 2, from tank 2 into tank 3, and out of tank 3; all at the given flow rate r gallons per minute. The initial amounts x1(0)= x0 (lb), x2(0) = 0, and x3(0) = 0 of salt in the three tanks are given, as are their volumes V1, V2, and V3 (in gallons). First solve for the amounts of salt in the three tanks at time t , then determine the maximal amount of salt that tank 3 ever contains. Finally, construct a figure showing the graphs of x1 (t) , x2(t) , and x3(t). r = 30, x0 = 27, V1 = 30, V2 = 15, V3 =10arrow_forwardConsider the initial value problem and find the solution for y''+4ay'+(4a²y+4y)=0 and y(0)=-2, y'(0)=-1.arrow_forward
- Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage LearningElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning