应该令u=x/y，然后积分，详情如图所示
求微分方程(y^2-3x^2)dy+2xydx=0满足初始条件x=0,y=1的特解
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求微分方程(y^2-3x^2)dy+2xydx=0满足初始条件x=0,y=1的特解
解题过程如下图：
求微分方程(y^2-3x^2)dy+2xydx=0满足初始条件x=0,y=1的特解 答案y^3=...
详细过程点下图查看
求微分方程(y^2-3x^2)dy+2xydx=0 x=0,y=1时的特解 步骤详细的加分
解：∵(y²-3x²)dy+2xydx=0 ∴((y\/x)²-3)dy+2(y\/x)dx=0...(1)设t=y\/x，则dy=xdt+tdx 代入(1)得(t²-3)(xdt+tdx)+2tdx=0 ==>x(t²-3)dt+(t³-t)dx=0 ==>(t²-3)dt\/(t-t³)=dx\/x ==>[1\/(1+t)-1\/(1-t)...
(y^2-3x^2)dy+2xydx=0,求通解.(讲出解题思路也可)
令u=x\/y即可，详情如图所示
(y^2-3x^2)dy+3xydx=0,y(0)=1
先积y，再积x ∫∫(x^2+3xy^2)dxdy =∫[-1-->1]∫[x²-->1](x²+3xy²)dydx =∫[-1-->1] (x²y+xy³) | [x²-->1] dx =∫[-1-->1] (x²+x-x⁴-x⁷)dx =1\/3x³+1\/2x²-1\/5x⁵-1\/...
(y^2-3x^2)dy+3xydx=0,y(0)=1
凑微分法 (x³-3xy²)dx+(y³-3x²y)dy=0 d[(x^4)\/4-1.5x²y²+(y^4)\/4]=0 (x^4)\/4-1.5x²y²+(y^4)\/4=C
求这个齐次方程组特解
解：∵(y^2-3x^2)dy+2xydx=0 ==>2xdx\/y^3-3x^2dy\/y^4+dy\/y^2=0 (等式两端同除y^4)==>d(x^2\/y^3)-d(1\/y)=0 ==>∫d(x^2\/y^3)-∫d(1\/y)=0 ==>x^2\/y^3-1\/y=C (C是积分常数)==>x^2=Cy^3+y^2 ∴此方程的通解是x^2=Cy^3+y^2 ∵当x=0时...
(y²-3x²)dy-2xydx=0,(y|x=0)=1 求特解,后面是当x=0时 ,y=1
设x\/y=u,dx\/dy=u+yu' （y²-3x²）dy-2xydx=0 (2u)du\/(1-5u²)=dy\/y 5dln│y│ +dln│5u²-1│=0 5x^2y^3-y^5=c c=-1
微分方程特解,要求有详细步骤!!
y^2dy-3x^2dy-2xydx=0 y^4dy-x^2dy^3-y^3dx^2=0 (1\/5)y^5-x^2y^3=c (1\/5)*1=c 特解为：y^5-5x^2y^3=1
