[next] [prev] [prev-tail] [tail] [up]

10.20   ODE No. 1875

{ddtx(t)+(ax(t)+by(t))f(t)=g(t),ddty(t)+(cx(t)+dy(t))f(t)=h(t)}

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

Mathematica: cpu = 0.007001 (sec), leaf count = 48 DSolve[{f(t)(ax(t)+by(t))+x′(t)=g(t),f(t)(cx(t)+dy(t))+y′(t)=h(t)},{x(t),y(t)},t]

Maple: cpu = 0.670 (sec), leaf count = 1633 {{x(t)=1(e12da−2bc(−a2+2da−4bc−d2da−bc(da−bc)+(a+d)−da+bc)∫f(t)−da+bcdt_C2−a2−2da+4bc+d2da−bc−da+bc+e−12da−2bc∫f(t)−da+bcdt(−a2+2da−4bc−d2da−bc(da−bc)−(a+d)−da+bc)_C1−a2−2da+4bc+d2da−bc−da+bc+∫−bh(t)(f(t))2−dg(t)(f(t))2+(ddtf(t))g(t)−(ddtg(t))f(t)(f(t))2e−∫f(t)dt2(−a2−2da+4bc+d2da−bc−da+bc−a−d)dte∫f(t)dt2(−a2−2da+4bc+d2da−bc−da+bc−a−d)−∫−bh(t)(f(t))2−dg(t)(f(t))2+(ddtf(t))g(t)−(ddtg(t))f(t)(f(t))2e∫f(t)dt2(−a2−2da+4bc+d2da−bc−da+bc+a+d)dte−∫f(t)dt2(−a2−2da+4bc+d2da−bc−da+bc+a+d))1−a2−2da+4bc+d2da−bc1−da+bc,y(t)=(d2b1−a2−2da+4bc+d2da−bc1−da+bc+1b(−12−a21−a2−2da+4bc+d2da−bc1−da+bc))e∫f(t)dt2(−a2−2da+4bc+d2da−bc−da+bc−a−d)∫−bh(t)(f(t))2−dg(t)(f(t))2+(ddtf(t))g(t)−(ddtg(t))f(t)(f(t))2e−∫f(t)dt2(−a2−2da+4bc+d2da−bc−da+bc−a−d)dt+(−d2b1−a2−2da+4bc+d2da−bc1−da+bc+1b(−12+a21−a2−2da+4bc+d2da−bc1−da+bc))e−∫f(t)dt2(−a2−2da+4bc+d2da−bc−da+bc+a+d)∫−bh(t)(f(t))2−dg(t)(f(t))2+(ddtf(t))g(t)−(ddtg(t))f(t)(f(t))2e∫f(t)dt2(−a2−2da+4bc+d2da−bc−da+bc+a+d)dt+(d22b1−a2−2da+4bc+d2da−bc1−da+bc+db(12−a1−a2−2da+4bc+d2da−bc1−da+bc)+2c−da+bc1−a2−2da+4bc+d2da−bc+1b(a221−a2−2da+4bc+d2da−bc1−da+bc−a2))_C1e−12da−2bc∫f(t)−da+bcdt(−a2−2da+4bc+d2da−bc(da−bc)−(a+d)−da+bc)+(−d22b1−a2−2da+4bc+d2da−bc1−da+bc+db(12+a1−a2−2da+4bc+d2da−bc1−da+bc)−2c−da+bc1−a2−2da+4bc+d2da−bc+1b(−a221−a2−2da+4bc+d2da−bc1−da+bc−a2))_C2e12da−2bc(−a2−2da+4bc+d2da−bc(da−bc)+(a+d)−da+bc)∫f(t)−da+bcdt+g(t)f(t)b}}

[next] [prev] [prev-tail] [front] [up]