求解答2道高数题1) x^3 = -i (i是虚数) 求x2) 解方程 x''+2x'-3x = 3t^2 - 4t已知:x(0)=1/3 , x'(0)=1
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![求解答2道高数题1) x^3 = -i (i是虚数) 求x2) 解方程 x''+2x'-3x = 3t^2 - 4t已知:x(0)=1/3 , x'(0)=1](/uploads/image/z/6950402-26-2.jpg?t=%E6%B1%82%E8%A7%A3%E7%AD%942%E9%81%93%E9%AB%98%E6%95%B0%E9%A2%981%29+x%5E3+%3D+-i+%28i%E6%98%AF%E8%99%9A%E6%95%B0%29++%E6%B1%82x2%29+%E8%A7%A3%E6%96%B9%E7%A8%8B+x%27%27%2B2x%27-3x+%3D+3t%5E2+-+4t%E5%B7%B2%E7%9F%A5%3Ax%280%29%3D1%2F3+%2C++x%27%280%29%3D1)
求解答2道高数题1) x^3 = -i (i是虚数) 求x2) 解方程 x''+2x'-3x = 3t^2 - 4t已知:x(0)=1/3 , x'(0)=1
求解答2道高数题
1) x^3 = -i (i是虚数) 求x
2) 解方程 x''+2x'-3x = 3t^2 - 4t
已知:x(0)=1/3 , x'(0)=1
求解答2道高数题1) x^3 = -i (i是虚数) 求x2) 解方程 x''+2x'-3x = 3t^2 - 4t已知:x(0)=1/3 , x'(0)=1
1)x³=-i x³+i=0
(x-i)(x²+ix-1)=0
x1=i x2=-i/2-√3/2 x3=-i/2+√3/2
2)设x=at²+bt+c+de^t
∵x(0)=1/3 ∴c+d=1/3
x'=2at+b+de^t
∵x'(0)=1 ∴b+d=1
x''=2a+de^t
代入x''+2x'-3x=3t²-4t
2a+de^t+2(2at+b+de^t)-3(at²+bt+c+de^t)=3t²-4t
∴-3at²+(4a-3b)t+2a+2b-3c=3t²-4t
-3a=3
4a-3b=-4
2a+2b-3c=0
∴a=-1 b=0 c=-2/3 d=1
∴ x=-t²-2/3+e^t
求解答2道高数题1) x^3 = -i (i是虚数) 求x2) 解方程 x''+2x'-3x = 3t^2 - 4t已知:x(0)=1/3 , x'(0)=1
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